Chairwoman Patty Murray at a Senate Budget Committee markup of the Concurrent Resolution on the Budget for FY2014. (Chris Maddaloni/CQ Roll Call)

On one side of the Capitol, President Obama sought to convince House Republicans on Wednesday that he is serious about reining in the rising cost of federal health and retirement programs.

But on the other side of the Capitol, Senate Democrats rolled out a 10-year spending plan that sent a different message: Not so fast.

While Democratic leaders are offering quiet support for Obama’s renewed campaign to strike a grand bargain with Republicans that would include cuts to Social Security and Medicare, a significant number of Democratic lawmakers are digging in their heels and vowing to protest any reduction in promised benefits.

That sentiment was on display Wednesday, as Senate Budget Committee Chairman Patty Murray (D-Wash.) announced a budget blueprint that proposes only minor trims to Medicare and Medicaid — the biggest drivers of government spending — and vows to make the cuts “without harming beneficiaries.”

Meanwhile, a growing number of Democrats have declared their opposition to a proposal that has emerged as Obama’s biggest selling point to Republicans: his offer to apply a less-generous measure of inflation to Social Security, resulting in slightly smaller annual cost-of-living increases.

“I don’t want to break the bad news to you, but the president is not the only elected official in the United States,” said Sen. Bernard Sanders (I-Vt.), a member of the Budget Committee, who pressed Murray to avoid any cuts to social programs in her spending plan. “Some of us believe very strongly that it would be absolutely wrong to cut Social Security benefits.”

Administration officials say Senate Majority Leader Harry M. Reid (D-Nev.) and House Minority Leader Nancy Pelosi (D-Calif.) are on board with the president’s push for a grand bargain and are willing to rally their rank and file to support politically touchy changes to health and retirement programs so long as Republicans sign off on significant new tax increases.

Obama got few complaints about his deficit-reduction plan during a lunchtime meeting Tuesday with Senate Democrats, administration officials said. But 107 House Democrats — more than half the caucus — have signed a letter declaring their “vigorous opposition to cutting Social Security, Medicare or Medicaid benefits.” And the complaints are likely to grow louder as Republicans press Obama for more details about his proposals to charge wealthy seniors more for Medicare coverage and to implement the Social Security inflation change, known as the chained consumer price index, or chained CPI.

That process is just now getting underway. In his meeting Wednesday with GOP lawmakers, Obama again outlined the offer he made in December to House Speaker John A. Boehner (R-Ohio) and more recently to more than a dozen Senate Republicans.

That proposal would replace $1.2 trillion in automatic spending cuts, known as the sequester, with $1.8 trillion in alternate policies over the next decade, including roughly $700 billion in fresh tax revenue. An additional $400 billion would come from reforms to Medicare, and $130 billion would come from applying the chained CPI to Social Security.

Republicans emerging from the meeting said the president was blunt about his willingness to pursue a deal over the objections of liberal Democrats. But he demurred, they said, when House Ways and Means Committee Chairman Dave Camp (R-Mich.) asked whether the White House would proceed with changes to entitlement programs without raising taxes.

“The president insisted that — this is how I would put it — that he would extract a pound of flesh from Republicans before he does that,” said Rep. Cory Gardner (R-Colo.). “I find that very frustrating.”

Noting that Democrats won a $600 billion tax increase in the Jan. 1 “fiscal cliff” deal, Gardner said, “Why can’t we move forward on some of these meaningful reforms?”

Republicans in the Senate are more willing to consider tax increases, but they are also pushing Obama more deeply into territory that troubles Democrats. The president’s proposal to cut Medicare leans more heavily on drug companies, hospitals and other providers than on beneficiaries.

But Sen. Tom Coburn (Okla.), one of a dozen GOP senators who dined with Obama at a downtown hotel last week, said Republicans oppose Obama’s biggest money-saver, a plan to reduce federal payments to drug companies by $140 billion over the next decade. And other dinner guests said they want to see more structural changes to reduce Medicare benefits.

Sen. Orrin G. Hatch (R-Utah) plans to press that point Thursday when Obama travels to the Capitol for a third straight day to meet with House Democrats and Senate Republicans. Aides said Hatch has prepared a list of health-care reforms he wants the president to consider, such as a higher eligibility age for Medicare, something Obama once supported but now opposes.

In the meantime, Senate Democrats are resisting the reforms the president has laid on the table. Instead of $400 billion in Medicare savings, Murray’s blueprint offers $275 billion from both Medicare and Medicaid. And instead of $700 billion in new tax revenue, her blueprint seeks nearly $1 trillion.

Murray offers additional spending cuts to the Pentagon and other programs, and her blueprint would slow the pace of government borrowing and stabilize the debt as a percentage of the economy.

But with annual deficits hovering around $500 billion for much of the decade, the debt would remain at historically high levels, rising from $16.7 trillion today to $24.3 trillion by 2023, or 94 percent of the nation’s economy.

As Murray’s Budget Committee began considering her proposals Wednesday, Sen. Mark R. Warner (D-Va.) argued — to the “consternation” of people “on my side,” he said — that Democrats will have to do more to prevent Social Security and Medicare from bankrupting the nation as the population ages.

“I share the belief of even my most progressive colleagues that Medicare and Social Security are among the greatest programs ever implemented. But I also believe that the basic math around them doesn’t work anymore,” Warner said.

“The longer we put off this inevitable math problem,” he said, “the longer we fail to come up with a way to make sure that the promise of Medicare and Social Security is not just there for current seniors but for those 30 years out.”

Paul Kane and Rosalind S. Helderman contributed to this report.