WASHINGTON » President Barack Obama’s budget overtures to Republicans may limit his bargaining power if the GOP ever returns to the negotiating table on a grand deficit-reduction deal.

In essence, Obama’s spending blueprint is a final offer, a no-budge budget whose central elements have failed to persuade Republicans in the past.

By voluntarily putting entitlement cuts on the table, particularly a proposal to slow the rise of Social Security benefits, Obama has no other gambit to win tax increases from Republicans.

With many Democrats balking at what he’s already offering, it’s not politically feasible for him to offer the GOP anything more.

Puzzled Democrats maintain that Obama not only has given away his leverage, he also has threatened the very identity of his party and the legacy of President Franklin D. Roosevelt, who signed the Social Security Act of 1935.

“If he’s trying to do it to show he is forthcoming as a negotiator, then why doesn’t he wait until he gets to the negotiating table?” said Rep. Rush Holt, D-N.J. “There’s a lot of talk about the fact that politically this is not a winner. Our brand is the party that brought you Social Security.”

What’s irked Democrats the most is Obama’s decision to include a significant shift in policy in his $3.8 trillion budget that would alter the government’s calculation of inflation, or the Consumer Price Index. If adopted, this new “chained CPI” would change the way the government measures inflation and would slow the rise in Social Security benefits and other programs.

In exchange, Obama is insisting on $580 billion in tax increases on wealthier taxpayers. It’s a demand that Republicans flatly reject.

The president has offered the benefit cut to Republicans before as part of broad deficit reduction negotiations, and only in exchange for tax increases the GOP stringently opposes. The White House says the same quid pro quo applies to Obama’s current offer, and chained CPI can’t take effect as a solo measure.

“You can’t decide to only pick out the concessions the president has made and not include the concessions that are from the Republican side, that need to be part of a bipartisan deal that could pass both houses,” said Gene Sperling, the top White House economist.

Faced with the withering criticism from Democratic and liberal allies, the White House has argued that the inflation proposal in the budget is a response to specific Republican demands during budget talks last year. “This is a Republican proposal,” White House spokesman Jay Carney insisted.

But the idea has been part of the thinking in Obama’s inner economic circle for two years, one the president put on the table during debt ceiling talks with the GOP in the summer of 2011.

Obama aides say the president had to include the Social Security change in the budget or risk being accused by Republicans of walking away from his previous offers. They say giving Republicans some of the entitlement cuts they seek means the GOP has one less reason to say no to the president’s proposals.

“The ball is now the Republican’s court,” said Dan Pfeiffer, Obama’s senior adviser. “Are they as serious about reducing the deficit as they claim to be?”

But placing the plan on a negotiating document is quite different from including the inflation proposal in the president’s budget, a document that turns his proposals from bargaining positions into actual policy proposals.

The White House tried to take the sting from the backlash by excluding from the new inflation formula those programs that are targeted to lower income people. Acknowledging that health care for older people increases at a higher rate than inflation, the proposal gives a bigger annual adjustment to older retirees.

Meeting with a dozen Republican senators for dinner this past week, Obama acknowledged the difficulties he would have selling Democrats on his proposal, according to participants.

Several senators said in interviews that Obama made a point of drawing attention to the criticism he was getting from his allies over the inclusion of the inflation measure in his budget.

“He did indicate a desire to work with us,” said Sen. Orrin Hatch of Utah, one of the guests. “But he also indicated that it’s very tough for him because of his side and their particular approach to things.”

Obama did win about $600 billion in tax increases in January, about half the total he was seeking.

Sen. John Thune of South Dakota, another dinner guest, said Obama’s budget shows that the president’s answer to lowering deficits remains taxes.

“Of course, Republicans feel like the tax issue has been settled,” he said. “In the end, in order to get something, the president is going to have to be willing to take on some of his constituencies and some of the groups that are in his ear all of the time. That’s going to be really hard.”

Jared Bernstein, former chief economist for Vice President Joe Biden, says the chained CPI inflation measure is a better gauge of inflation for the general population. But he has advocated for a separate formula for the elderly that takes into account faster growth in the cost of health care. He doesn’t quarrel with the policy, but says it was risky for the White House to place it in the budget.

“Strictly as a bargaining tactic, I would have held it until I needed it,” he said. “This only works as a tactic if the White House absolutely sticks to its position that this is not a menu, otherwise it’s pretty terrible.”

Addressing that concern, Carney said that when it comes to Obama’s proposal, “the whole approach has to be embraced.”

“It is not a starting point,” he said. “It is a sticking point.”

Many Democrats remained unconvinced. “I don’t think this is a negotiating strategy,” said Rep. Louise Slaughter, D-N.Y.

Asked what she thought it was, she replied: “I have no idea.”