President Barack Obama led a pep rally for his signature health law at the White House on Monday. He managed to gather a grateful few who navigated a cyber morass and signed up for coverage, no small feat. But he also conceded the computer troubles many others have had: “Nobody’s madder than me about the fact that the website isn’t working as well as it should, which means it’s going to get fixed.”

Health and Human Services Secretary Kathleen Sebelius promises a “tech surge” — enlisting the “best and brightest” cyber experts to fix the balky website. She also grudgingly agreed Monday to testify before a House committee about the Obamacare website problems. That, at least, answers critics who rightly pointed out that she had time to appear on Comedy Central’s “The Daily Show” but no time for the U.S. House of Representatives.

The technical problems with Obamacare are broad, deep and humiliating to the administration, which promised a “first-world” experience only to deliver something not even in the galaxy.

The computer problems may be fixed in weeks or months — although as the nation learns more about the extent of those computer problems, there’s far less confidence that a fix will come soon … or ever.

But the problems with Obamacare go much deeper than a few million lines of faulty code and a sign-up system that swallows enrollee applications in a single electronic gulp.

The bugs aren’t just in the software. They’re in the law itself.

Consumers are finally seeing insurance rates and plans. In many cases, insurance premiums, deductibles and co-pays are rising. Illinois officials said premiums here would be lower than expected. But a Tribune analysis of 22 of the lowest-priced plans showed that those plans required huge annual deductibles of more than $4,000 for an individual — and $8,000 for family coverage.

Lower premiums also come with a troubling tradeoff: access to a narrower networks of hospitals and doctors. If people aren’t careful in choosing coverage, they may be shocked to find they have to pay much more for out-of-network care to go to their preferred doctor or hospital.

Individuals who already have coverage are learning they can’t keep it after Jan. 1. They must choose a new health plan, which may come at considerably higher cost than they’re paying now.

This puts at risk the basic underpinning of the law: that the legal requirement on individuals to buy health insurance will provide high even revenue and a broad enough risk pool to cover the cost of health care for older people and others who have chronic health conditions.

The greatest appeal of Obamacare is that it provides access to people who couldn’t find insurance. But for Obamacare to work, for insurers to continue coverage, millions of healthy, younger Americans must sign up. Their premiums help pay the costs of covering older, sicker people. If the healthy don’t sign up, if they choose instead to pay a modest penalty, the entire system could plunge as costs rise, insurers pull out, and markets collapse.

There are more Obamacare unknowns out there: Federal judges in Washington, D.C., and Virginia are deciding if the law actually prevents the federal government from offering premium subsidies to low- and middle-income Americans in Illinois and 35 other states. If so, millions of people could be required to pay much more for insurance — or could just walk away.

There was no acknowledgment of these issues Monday from Obama or Sebelius. But they’re going to have to deal with them. To do that, they’re going to have to cooperate with their harshest critics in Congress.

Fixing the computer software won’t fix the profound problems with Obamacare. That’s beyond the pay grade of the techies.

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