Much has been written about Bill Daley’s selection as White House chief of staff, a position sometimes called “Chief Javelin Catcher” (a title whose accuracy one of us strongly affirms). Most agree that Mr. Daley is the perfect choice to help President Obama set a new tone for his presidency. He is a moderate, strongly rooted in Democratic principles and politics. Though he comes from the business community, he is no colorless technocrat or Republican shill. He is a Daley from Chicago and will not forget the needs of the lunchbucket voters who’ve supported Daleys for 50 years, or the political lessons he learned at the knee of his father, Mayor Richard J. Daley.

Mr. Daley will need all his political skills to tackle what we think should become one of the signature accomplishments of his tenure: the return of liberalized trade as a centerpiece of Democrats’ vision of economic competitiveness and globalization.

Bill Clinton embraced this vision, and he understood that trade liberalization required strong bipartisan efforts. To pass the North American Free Trade Agreement (Nafta) in 1993, we set up a bipartisan war room within the White House, headed by Bill Daley and former Republican Congressman Bill Frenzel. Messrs. Daley and Frenzel worked together, with the full support of the president and White House staff, to push Nafta through the House with 102 Democratic and 132 Republican votes, and on to an equally bipartisan total in the Senate.

Liberalized trade was also at the heart of President Clinton’s view that America needed international competition to succeed in an increasingly trade-dependent world. Not every Democrat supported this view, though Mr. Clinton strongly pushed it within the party.

But we quickly lost this bipartisan consensus and the progress Mr. Clinton had forged in his own party. By 1997, when Mr. Clinton sought renewal of “fast track” authority to negotiate more trade agreements, Republican Speaker of the House Newt Gingrich could not corral his majority to support the president and the effort failed. And although President George W. Bush did manage to make congressional headway on trade with his Republican majorities, he did so principally with Republican support.

In the first two years of President Obama’s tenure, progress on trade was largely frozen. Mr. Obama stated his support for the uncompleted pieces of the Bush trade agenda—free trade agreements with South Korea, Panama and Colombia, the dangling Doha World Trade Organization round, and Russia WTO accession—but little measurable progress was made.

Now, in a few short weeks, Mr. Obama has renegotiated the U.S.-Korea free trade agreement and announced that it will be a priority in the new Congress. He has taken steps to resolve a longstanding trade dispute with Mexico over trucks that goes back to the Clinton years. And, with his selection of Mr. Daley, the president has hired the man who can make this trade revival a reality.

What now? Our experience tells us that the only way to push a major trade agreement through Congress—even one where the nominally pro-trade GOP rules the House—is with strong and unyielding presidential leadership, a unified White House staff and cabinet, and a genuinely bipartisan approach to stakeholders and the Congress.

First, the president must be fully committed. Nafta was a bipartisan success in no small part because of the personal involvement of Mr. Clinton and sometimes tortuous negotiations with members of Congress. It’s true that some pork was doled out and more than one bridge was built as a result of a Nafta vote—something they probably still understand in Chicago.

Second, the White House and cabinet must be unified in pulling for passage. Everyone from Vice President Joe Biden to Secretary of State Hillary Clinton to Labor Secretary Hilda Solis and U.S. Trade Representative Ron Kirk must be fully engaged, without hesitation. Don’t forget the crucial role that then-Vice President Al Gore’s 1993 debate with Ross Perot played in swinging public opinion in favor of Nafta.

Third, the effort must be genuinely bipartisan. We’ll need scores of members from both sides to make passage possible (this is particularly true with a large tea party GOP caucus that is as yet undefined on trade). Perhaps Mr. Obama could even take a page from the 1993 playbook and bring into the White House a prominent Republican—former U.S. Trade Representative Carla Hills, former Reagan Chief of Staff Ken Duberstein, or a former congressman such as Jim Kolbe or Chris Shays, for example—to help quarterback the effort.

Finally, the president has to show that his commitment to the U.S.-Korea free trade agreement isn’t a one-off. Moderates and independents who have been spooked by an economic approach they see as veering strongly to the left are looking for signs that this president embraces their centrist views. A commitment to deficit reduction, sustained outreach to business, and a genuine embrace of trade liberalization must go hand-in-hand. Most importantly, the president should commit to advancing the pending trade agreements with Colombia and Panama right now, instead of leaving them until later as some in his administration would prefer. Why bother taking a half-measure on trade?

A full-throated campaign for the Korea, Colombia and Panama trade agreements, along with WTO accession for Russia, can help reset this presidency. Capitalizing on his selection of Mr. Daley with a renewed American trade policy, Mr. Obama has the chance to remind moderates in both parties and independent voters that he is the man they voted for in 2008—a leader who appreciates the goals of businesses large and small, and who sees America as confident and innovative enough to remain the global economy’s True North.

It also gives the president the opportunity to strengthen ties with longtime allies who cultivate liberal democracy, reject old and ugly political and social traditions, stand shoulder-to-shoulder with us when it comes to fighting the world’s darkest forces, and are willing to open their markets to us—or in the case of Russia, to encourage that behavior. It won’t be easy, and it may alienate some in the Democratic base, but it is essential.

Mr. McLarty was chief of staff to President Clinton in 1993-94 and helped bring Bill Daley into the White House to lead the 1993 Nafta ratification effort. Mr. Cunningham was an aide to President Clinton and to then-Sen. Joseph Biden.