WASHINGTON (CNN) -- President Obama huddled with Senate Democrats on Capitol Hill Wednesday as the White House fought to save major domestic priorities in its record $3.6 trillion budget from the congressional budget ax.
President Obama visits Capitol Hill on Wednesday to sell his budget to congressional Democrats.
Key budget votes are expected in the Senate and House later this week.
Obama's visit to the Hill came shortly after Senate Budget Committee Chairman Kent Conrad, D-North Dakota, trimmed the president's proposal in response to congressional projections showing larger-than-expected budget deficits over the next several years.
Obama has pledged to cut the deficit in half within five years.
"We had a very comfortable meeting with President Obama," said Senate Majority Leader Harry Reid of Nevada. "He made us all feel content and inspired by where we need to go."
Reid said he is confident the full Senate will pass Conrad's version of the budget next week.
Conrad said he had preserved the president's major initiatives in education, energy and health-care reform in the wake of "new realities" on finances without sacrificing the administration's deficit reduction goals.
Multiple senators said the Democrats' meeting with Obama was cordial, and that the president said he understood that the budget process would require compromise on all sides.
Oregon Sen. Ron Wyden and Louisiana Sen. Mary Landrieu said the most pointed questions Obama got were about how he can undertake large initiatives in energy and health care reform during difficult economic times.
Obama repeated an argument he has made in recent weeks, saying that smarter investments in core priorities now will ultimately help control costs later. The president said initiatives such as health reform and economic reform are linked, according to Wyden. Watch more on the Obama budget »
"He reiterated what he said before," Indiana Sen. Evan Bayh told reporters. Namely, that "he never had [any] expectation that the budget would be rubber stamped ... and he fully expected members of the Senate to come forward with their ideas about how to improve the process."
Conrad and other centrist Democratic senators, whose support is critical to passing the legislation, had raised concerns about the long-term impact of the president's spending plan on the federal deficit.
In a letter to the Senate Budget Committee dated Tuesday, 12 of the 16 members of the centrist Senate Democratic coalition, which calls itself "the moderate Dems Working Group," expressed concerns about the direction of the president's $3.6 trillion budget.
The lawmakers noted the Congressional Budget Office's projection of a cumulative deficit over the next 10 years of $9.3 trillion, "roughly $2.3 trillion higher than the president's budget had assumed."
While acknowledging the economic and fiscal distress the Obama administration has inherited, the 12 moderates said the deficit projections "are not acceptable."
The senators who signed the letter were: Bayh, Landrieu, Sen. Tom Carper of Delaware, Sen. Blanche Lincoln of Arkansas, Sen. Mark Pryor of Arkansas, Sen. Kay Hagan of North Carolina, Sen. Jeanne Shaheen of New Hampshire, Sen. Herb Kohl of Wisconsin, Sen. Claire McCaskill of Missouri, Sen. Bill Nelson of Florida and Sen. Mark Begich of Alaska. Sen. Joe Lieberman, formerly a Democrat and now an independent from Connecticut, also signed the letter.
Publicly, the administration has tried to minimize differences between Obama's budget proposal and changes sought by congressional Democrats.
The "House and Senate budget committees are taking up resolutions that are fully in line with the president's key priorities for the budget," White House Office of Management and Budget Director Peter Orszag said in a conference call Wednesday morning.
"There have been some changes made ... but they are 98 percent the same as the budget the president sent up in February."
Obama, in a news conference on Tuesday, defended his budget, saying the plan he proposed is "inseparable" from the overall strategy for economic recovery.
Obama brushed off those skeptical of the scope of his investments, saying, "We haven't seen an alternative budget out of them."
Republicans, who blasted the Obama budget proposal because it "spends too much, taxes too much and borrows too much," according to Senate Republican Leader Mitch McConnell of Kentucky, have also criticized Conrad's proposal because some of the items Conrad stripped from the spending blueprint might have to be funded anyway.
For example, Conrad's budget strikes Obama's proposal to set aside $250 billion in case more money is needed for the financial sector rescue, an aide said.
Conrad's budget also curtails Obama's fix of the costly alternative minimum tax and doesn't account for increased payments for doctors who care for Medicare recipients, said Sen. Judd Gregg of New Hampshire, the top Republican on the Budget Committee.
"You can get these presidential numbers down by using a lot of gimmicks that the president didn't use. That would be a mistake. Let's be honest with the Americans," Gregg said Tuesday.
"It's certainly not a gimmick," Conrad responded Tuesday. "We faced up to changes."
CNN's Ted Barrett and Louise Schiavone contributed to this report.