It is now a daily routine: President Obama issues another class-warfare call to arms, demanding that the rich pay higher tax rates starting next year. Along the way he also takes derisive shots at Republicans in Congress, as Mr. Obama insists that they triple income- and investment-tax rates for the affluent next year.

His primary adversary in accomplishing that goal if he wins re-election is likely to be one of those Republicans in Congress: Dave Camp, chairman of the House Ways and Means Committee. Mr. Camp ridicules Obama’s plans as a bullet aimed at “small businesses and investors, which will only further weaken the fragile economy.”

His twin goals are, first, to back America away from the 2013 tax cliff “so that no one’s taxes go up,” and second to pass tax reform, creating what he calls “a fairer, flatter and simpler tax code that lowers rates, gets rid of lobbyist loopholes, and creates more growth and jobs.” Those two goals are pretty much the polar opposite of what the president is seeking.

The surprise is that Mr. Camp remains upbeat about accomplishing both, including finally cracking the code on tax reform by the end of next year. It’s a sure thing if Mitt Romney wins, he thinks, and even possible in a second Obama term. “The next president, no matter who that is, is going to have to lead on this issue,” he insists.

This is certainly a minority opinion—so why the optimism? “We’re facing a train wreck with the tax system in 2013. Pretty much the whole tax code expires next year—the expiration of the Bush tax cuts, the Alternative Minimum Tax hitting the middle class, the estate tax, and all the rest. Given the weakness of the economy, voters are going to demand that we get this done.”

Most Americans have never heard of Mr. Camp, who is still boyish-looking at age 59 and is in his 11th term representing northern Michigan. Compared to the many flamboyant predecessors who swung the Ways and Means gavel—Charles Rangel, Bill Thomas, Dan Rostenkowski—Mr. Camp is soft-spoken, laid-back and collaborative. He was recently diagnosed with what he calls a “treatable” form of non-Hodgkins lymphoma. He pledges this illness won’t sidetrack him from his congressional goals. And there’s no doubt he knows the tax code inside and out.

Listening to him talk leaves little doubt that he wants tax reform to be his legacy: “It is my absolute highest priority.” Thanks to term limits on committee chairmen, he has only two more years to get it done. “I want something that will be pro-growth and last for years if not decades, so we’re not destabilizing the economy by putting the tax code up for grabs every two years,” he says.

If Mr. Obama wins re-election, that’s going to be a heavy lift.

So how to do it? The model Mr. Camp has in mind happened 26 years ago, the last time Congress had the fortitude to look under the hood of the tax code and clean the engine. The Tax Reform Act of 1986 was negotiated by the Reagan administration, Democratic Rep. Dan Rostenkowski and Republican Sen. Bob Packwood. It was one of the true bipartisan triumphs of modern times, passing with 97 Senate votes, including those of current Senate Democratic leaders Harry Reid and Charles Schumer.

The 1986 tax reform eliminated most special-interest deductions and loopholes, lowering the top income-tax rate to 28% from 50%. Harvard economist Dale Jorgenson says the gains to economic growth from the lower rates and the simplified code increased GDP by more than $1 trillion, and that a similar reform now could increase national wealth over the long term by $7 trillion in net present value.

But in the 1990s and 2000s Congress began tinkering again, a lot of the junk removed from the code “has been put right back in,” and tax rates started rising. Mr. Camp’s calculates that “we’ve made 5,000 changes to the tax code just in the last 10 years.” He says the whole system is so complicated that even the corporate lobbyists who form long lines outside his office seeking tax favors “are now telling me, ‘Please fix the code. Give us less paperwork and a 25% rate and we’ll gladly give up our loopholes.'”

Although he likes the flat tax that Steve Forbes popularized 16 years ago, his draft plan calls for two rates—10% for most Americans and 25% on six-figure earners and above. To ensure that tax reform gets a fair hearing, he says Republicans plan to create a “fast-track” authority so that the compromise doesn’t get bogged down in committees and is assured an up or down vote on the House floor.

“We’re not competitive on taxes anymore, especially in terms of international tax,” he says. “We’ve got the highest corporate rate in the world, and we’re the only country left with a world-wide system of taxation. We need to be on the cutting edge of tax and economic policy in the world so that we’re the center of innovation, effort, growth, jobs.”

On the business side, he wants to bring the corporate rate down to 25%, paid for by eliminating certain deductions and green energy tax subsidies “so we’re not constantly picking the energy flavor of the month,” and perhaps eliminating the tax advantages of debt financing over equity. This would no longer allow businesses to deduct the interest on their borrowing.

He’s also considering a low “deemed repatriation tax” that would require American companies to pay a tax of about 5% on profits stored overseas. “We think that will help raise money and bring back cash stored offshore,” because the rate would be so much lower than what is charged today. Then he adds: “I’m much more interested in raising revenues for businesses than for the government.”

The hard part of tax reform is bringing the special interests to heel while taking away popular deductions. Can we eliminate all such deductions? Here Mr. Camp bobs and weaves. On the mortgage-interest deduction: “You probably picked the toughest one, because most families have a mortgage. And that is the largest savings vehicle for most families.”

I couldn’t get him to specify what deductions he would put on the cutting board: “I think at this stage of the game, it is not good to legislate body parts,” adding that “you don’t have to reduce or hit all of the deductions.” I take that as a roundabout admission that the GOP may flinch when it comes to deductions that are the biggest revenue losers.

Mr. Camp has sought advice from Mr. Packwood, who helped engineer the 1986 reform. The major lesson he took away is, “You’ve got to do it in a bipartisan way.” But can bipartisanship happen if Democrats won’t cut tax rates but want to raise them instead? Where are the Bill Bradleys, the Richard Gephardts, and other Democrats who once wanted lower rates and a broader base?

Mr. Camp still sees some hope, pointing to the 34 Democratic senators and 91 House Democrats who voted for the 2010 extension of the George W. Bush tax rates. The obvious Democrat to take the role of Bill Bradley would be Max Baucus, the Senate Finance chairman. Mr. Camp will only say that Mr. Baucus is “open-minded” on tax reform, hardly a hearty endorsement.

Mr. Camp adds that a crucial precondition to tax modernization is to “fix the revenue scoring system to take full account of the economic growth dividend from simplification and lower rates.” Republicans have been saying that for years. Yet they have never made the Joint Tax Committee or the Congressional Budget Office change their rules to take account of how worker and investor behavior changes when tax rates change.

As in 1986, “we will use a revenue neutral model,” Mr. Camp says, and “we’re not trying to find ways to address the debt or deficit through tax reform.” He sounds like Jack Kemp here insisting that “growth will bring more revenues and our target is to have a tax system that raises revenues of between 18 and 19% of GDP.” That’s up from about 16% today. Who says Republicans won’t raise tax revenue?

Mr. Camp is also confident that after the election in November he can get a deal with Democrats to extend all the current tax rates, including for those who make more than $200,000. “I think we can get bipartisan support,” he says, citing comments from former President Clinton and four Democrat senators who expressed support for extending current tax rates. Why would Democrats budge? “Because the economic cost of not getting it done is too high,” he replies. I wish I shared his optimism.

Where Mr. Camp is less upbeat and visibly frustrated is on the prospect of fundamentally fixing entitlements. “There really is a wide divide on how that issue is looked at by the Republicans and Democrats. I’d hate to paint with a broad brush, but many Democrats don’t feel that we have a crisis in entitlements and Republicans do.”

Mr. Camp is contemptuous of the Democratic inclination to “demagogue every Republican proposal,” such as last year’s Democratic television ad showing a Republican tossing an elderly woman in a wheelchair off a cliff. He dismisses out of hand the standard Democratic fix of squeezing doctors and hospitals on reimbursement rates: “This only exacerbates the problems and makes it more difficult for seniors to find Medicare physicians who’ll treat them.”

With a $16 trillion debt and trillions more in unfunded liabilities embedded in these programs, does he think it is getting too late? “I’m an optimist, I think we are still at a point where if we act, we can address these problems before it’s a situation like Europe. They may be past the tipping point.”

The trick for Mr. Camp to realize his dream of creating a pro-growth, comprehensible, 21st-century tax code is not just to get Democrats to agree to lower tax rates, which will be hard enough. Even tougher may be to get Republicans to give up those popular deductions and carve-outs that many in the middle class and Chamber of Commerce have come to regard as rights.

“Every deduction was put in there for a reason and has powerful lobbies behind them,” he admits. “I’m trying to work my way out of a job.” If he does, everyone will know his name.