Obama reiterated the pledge in a "CBS Evening News" interview with Katie Couric on Tuesday, saying: "It's got to be deficit neutral. It can't add to our deficits." (See more from the interview)
So what of the Congressional Budget Office's conclusion that the House bill does add to the deficit?
Democrats and the Obama administration argue that the $245 billion included for doctors - the approximate 10-year cost of adjusting Medicare reimbursement rates so physicians don't face big annual pay cuts - does not have to be counted in the overall cost of the health care bill.
Their only-in-Washington reasoning is that they already decided to exempt it from congressional "pay-as-you-go" rules that require new programs to be paid for. In other words, it doesn't have to be paid for because they decided it doesn't have to be paid for.
The administration also says that since Obama already included the so-called "doc fix" in his 10-year budget proposal, it doesn't have to be counted again in the health overhaul bill.
"It so happens they added that to this piece of legislation, but that's sort of already baked into our fiscal trajectory," White House budget director Peter Orszag said last weekend on "Fox News Sunday."
"We're looking at what's happening with regard to new policy," Orszag added. "And with regard to new policy, this is deficit neutral over the first decade."
Old policy or new, no one disputes that the "doc fix" does in fact add to the deficit. And the administration's position carried no weight with the CBO when it released its analysis of the House Democrats' bill.
The CBO, Congress' nonpartisan budget scorekeeper, said Friday that enacting the legislation "would result in a net increase to the federal budget deficit of $239 billion over the 2010-2019 period." The increase is mostly because of Democrats' failure to pay for the "doc fix," but CBO didn't even bother to entertain the notion that its cost should be excluded.
The response from House Democrats? A wave of triumphant press releases claiming - misleadingly - that CBO's estimates backed up their claims that their bill was deficit neutral.
The issue is providing ammunition for Republicans, who are accusing Obama of breaking his deficit-neutrality promise. And health experts scoff at the Democrats' fuzzy math.
"Of course it adds to the deficit," said Alex Vachon, a health policy analyst. But at the same time, Vachon and others give the Obama administration and congressional Democrats some credit for attempting to permanently fix the doctor payment issue.
Since its enactment in 1997 the so-called "sustainable growth rate" mechanism, which uses a complex formula to establishes annual target costs for physicians' services under Medicare, has not kept up with actual costs.
That's required Congress to step in almost annually with one-year fixes to prevent doctors from facing ever-bigger potential cuts in payment rates. The cut that loomed for doctors in 2010 was 21 percent. Without a permanent redo of the payment formula, Congress would presumably have had to continue to do one-year fixes, something that would also have cost money and that doctors hated because of the uncertainty involved.
The "doc fix" has been a top priority for the American Medical Association, which cited its inclusion as a key reason for its endorsement of the House Democrats' sweeping health care bill.
In the Senate, Finance Committee Chairman Max Baucus, D-Mont., who is presiding over negotiations aimed at a bipartisan agreement on health care, said the issue of paying for the "doc fix" has not yet come up in the talks.
Robert Laszewski, a former insurance company executive who's now a consultant to industry, contended doctors were "paid off" to support the House bill.
"The AMA would not have endorsed the House bill without the doc fix," Laszewski said. "The fact that the CBO has said the doc fix would add hundreds of billions of dollars to the cost of the bill makes clear how much it is worth to the docs."
Asked to comment, the AMA provided a written statement from the group's president, Dr. James Rohack: "Expansion of health care coverage, elimination of denials for pre-existing conditions and repeal of the flawed Medicare physician payment formula are all reasons the AMA supports the House bill."