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In the London Underground, a recorded voice warns travelers to “mind the gap” between an incoming train and the station platform. The phrase became so popular that it has spawned a book, a TV quiz show and countless T-shirts.

As President Obama tries to overhaul the health-care system, he actually has to mind two gaps: a treasury gap and a trust gap. Either one could derail his ambitious plans to cover the 47 million Americans who lack health insurance.

Without a doubt, there are some positive signs. At a White House meeting this week, major players in the health-care industry — doctors, drug makers, insurers, hospitals — pledged to reduce the rapid rise in health-care costs by 1.5 percent a year for 10 years. Since health care accounts for about 17 percent of the entire American economy, those savings could, in theory, amount to $2 trillion.

Obama has clearly made headway with his argument that everyone suffers from spiraling health costs. In the latest Kaiser Family Foundation survey, 59 percent said health-care reform is more important than ever, while only 37 percent called it too costly in the current economy.

Still, skepticism is the only sensible mindset when it comes to reform. Obama went way overboard in using words like “historic” and “watershed” to describe his White House meeting. He forgot to mind the gaps.

Start with the treasury gap. Just as Obama was lavishing praise on health-care executives, his own budget office reported that this year’s deficit would surpass previous estimates and reach $1.84 trillion. A day later, trustees warned that Medicare was facing a “significantly less favorable” financial outlook. And yet the president still insists he can find the $1.5 trillion needed to finance his reform proposals. His “watershed” is looking a bit more like a cold shower.

It’s certainly encouraging that health-care executives feel compelled to promise a cost-reduction effort, but frankly, we’ve heard all this before. Many times. When we started covering Congress in the late 1970s, “hospital cost containment” became a major buzzword, but it never happened. Henry J. Aaron, an economist at the Brookings Institution, captured our feelings in The New York Times: “I had a Rip Van Winkle moment, as if I had fallen asleep in 1977 and woke up again this morning.”

As Aaron’s comment indicates, confidence might be in shorter supply than cash. And that lack of trust centers on one key element of the debate — whether to create a public insurance plan that competes with private companies.

Supporters of the idea are absolutely convinced — or so they say — that without a public plan influencing the marketplace, private insurers will never provide adequate coverage for high-risk or low-wage families.

The trust gap is equally wide on the other side. Critics of a public plan are absolutely convinced — or so they say — that federal intervention in the market can lead to only one outcome: nationalization of health care. No matter that Obama has insisted repeatedly that a government-run system is off the table. His critics refuse to believe him.

If he’s going to succeed, Obama has to isolate the ideologues on both sides: the far left that really wants a government-run system, and the far right that really wants no change at all.

Obama has to explain, honestly, how he’s going to finance his reforms. And he has to embrace, honestly, a public plan that preserves the free market and precludes a national takeover. Otherwise, the gaps could swallow him up.

Steve and Cokie Roberts can be reached at stevecokie@gmail.com.