President Obama said Monday that his budget proposals will take the country "almost all the way to covering the full cost of health care reform," as he battled innate cynicism in Washington over his ability to pass sweeping health care legislation this year without adding to the deficit. 

In an address to the American Medical Association in Chicago, the president reiterated that the program will be "fully paid for," and that the $950 billion in savings and revenue that he's put forward will just about get there. He said he'll work with Congress to "make up the difference" in the coming months. 

"I know people are cynical about whether we can do this or not," Obama said. "I also know this -- we can't let this moment pass us by." 

Lawmakers, however, don't have quite as firm a handle on how they'll fulfill Obama's call. 

Though Obama has outlined nearly $950 billion offset the cost of a program tagged at about $1 trillion over the next decade, some fear the actual price tag could be much higher and question whether Obama's estimates about a coming windfall in government savings are accurate. 

"I think they bear little resemblance to reality," Michael Tanner, senior fellow at the Cato Institute, said of Obama's proposals. "This is the budget that makes George Bush look like a CPA." 

Tanner cited alternate cost projections for health care reform ranging from $1.2 to $2 trillion over the next decade. 

Obama claims to have the money on the table, with potential wiggle room for a rising price tag. 

His White House is proposing a $635 billion "down payment" on health care reform, with half of that financed by revenue proposals including a limit of the value of itemized deductions for families earning over $250,000 a year. The other half is Medicare and Medicaid savings -- and this past weekend, he outlined another $313 billion in savings through Medicare and Medicaid. He's resisting calls to tax health care benefits, though the idea does not appear to be off the table. 

"Real reform will mean reductions in our long-term budget," Obama said in his weekly radio address on Saturday.  

On Monday, Obama repeatedly stressed that the $950 billion amount does not include "longer-term savings" from prevention programs and other strategies -- in other words, the difficult-to-estimate savings that budget geeks can't score with any degree of accuracy. 

But even if the plan, which includes a controversial and costly government-run public option, holds to $1 trillion, Tanner said lawmakers and the Obama administration still need to find better and more realistic ways to offset the cost. 

"Politically I don't see any of it as realistic," Tanner said, noting that the itemized deduction proposal is politically difficult and the calls to draw savings out of Medicare and Medicaid would trigger opposition from the medical lobbies. 

Some senators have deemed the deduction proposal dead on arrival, fearing the possible negative impact on an already-depressed housing market, as well as a decrease in charitable giving.

Obama tried to address some of the concerns over Medicare and Medicaid Monday before the AMA, arguing that his plan, including the public option, would ultimately be good for business. 

Meanwhile, lawmakers are reaching a consensus on a couple matters -- namely, that the current system is unsustainable and that it will cost a lot to fix. 

"It's going to be a lot," Senate Majority Whip Dick Durbin, D-Ill., said Sunday on CBS' "Face the Nation. "I think the president has shown good faith in coming forward with $600 billion. Now it's up to Congress to find its way for the rest of the revenue and to really change our health care system." 

Senate Minority Leader Mitch McConnell, R-Ky., said the Finance Committee is "beginning to look at how you would pay for this massive expansion of health care." 

"We're having a hard time paying for the health care -- the government health care we already have, Medicare and Medicaid. Now they're trying to grapple with how to pay for the expansions," he said on the same program. "It will not be easy." 

Lawmakers have toyed with other ways to finance health care reform, including an extra tax on sugary -- and alcoholic -- beverages. Such proposals could pay for a fraction of the reform package. 

McConnell was loath to talk about tax increases "at the outset." 

But that may be where the debate leads. Key lawmakers, including Democrats, are pushing another potentially more valuable idea to tax employer-provided health care benefits. 

Though it is not particularly popular -- rank-and-file Democrats are worried about the political ramifications of embracing a tax that will no doubt hit middle-class Americans -- it is expected to be part of a health care overhaul bill Senate Finance Committee Chairman Max Baucus, D-Mont., will present to his panel Wednesday. 

Sen. Charles Grassley, ranking Republican on the Senate Finance Committee, told "FOX News Sunday" that Obama should take a serious look at such a proposal. 

"For the benefit of making this bipartisan, presidential leadership in this area would be very good," Grassley said. 

The problem with that is Obama fiercely opposed the idea when his former rival, Sen. John McCain, R-Ariz., proposed it on the campaign trail. 

So far, the administration is holding to that resistance. 

"We made it clear that we do not think that it is the way to go," Vice President Biden said on NBC's "Meet the Press. "We think that is the wrong way to finance this legislation." 

Kathleen Sebelius, secretary of the Department of Health and Human Services, told ABC's "This Week" that such a plan would have a "huge potential of destabilizing the private market and leaving more Americans uninsured," as it could discourage employers from offering health care to employees. 

Sen. Chris Dodd, D-Conn., speaking on "FOX News Sunday," also called the idea "unnecessary." 

Though Baucus is trying to sell Obama on the need to tax some benefits, Dodd said money in the budget, coupled with other cost-reduction measures, would make such a proposal excessive. 

He said lawmakers should take a close look at Obama's latest proposals to save $313 billion over 10 years through cuts to Medicare, Medicaid and other programs. Plus he said eliminating unnecessary tests and exams, and improving prevention programs, will help fill in the rest. 

But while Obama officials reject the idea of taxing benefits, they're not ruling out accepting a bill that includes the mechanism. 

"We'll have to see what the whole bill says," Biden said Sunday. 

In the end, Obama's oft-repeated mantra of not making "the perfect the enemy of the essential" might come into play. 

"I think the Obama administration will ultimately do whatever it takes to pass it," Tanner said. "They are willing to compromise -- I don't know if Congress is willing to make a deal." 

FOXNews.com's Judson Berger and FOX News' Trish Turner contributed to this report.