Chief correspondent

With House Speaker John A. Boehner’s decision to back away from a “grand bargain” on the budget, President Obama may be forced to recalibrate his goals and his strategy to show that he can bring the negotiations to a successful conclusion.

Throughout the spring and the summer, he has tried to set himself apart from Republicans and many Democrats as the leader most determined to solve a big problem with a big solution and as the politician most willing to make real compromises to get there.

Republicans have criticized Obama as coming to the table late — a charge his advisers reject. The president and his team think that the harder he pushes for a $4 trillion agreement that would include spending cuts and new taxes, and the more Republicans resist such increases, the more he will command the politically valuable center in the debate.

That continues to be his public posture, but that may no longer be a practical strategy in the negotiations. The president needs to wring concessions out of Republicans that they have been unwilling to make, while reassuring his Democratic allies that he is not giving away more than necessary to get a deal.

Obama continued to walk a political tightrope on Monday, prodding Republicans to accept more taxes as part of any budget deal while making clear that he is prepared to endorse potentially major cuts to Medicare and other entitlements — a move Democrats oppose — to get a far more significant agreement.

The president delivered twin messages during a news conference on Monday. The first was to renew his call, despite Boehner’s announcement on Saturday, for an agreement that would provide a long-term solution to the country’s debt and deficit problems, rather than a more modest deal that probably would include neither entitlement nor tax reform.

With an eye on Republicans who are balking at major concessions on taxes and revenue, the president said: “Now is the time to deal with these issues. If not now, when?”

His second message was aimed at Democrats, in Congress and nationwide, who continue to warn him not to touch Medicare or Social Security and who worry about whether he has the backbone to stand up to Republican demands.

To those Democrats, Obama said that, without reforms, Medicare and Social Security will not be able to meet their obligations and that, unless the country solves its long-term fiscal problems, there will not be enough money to fund the programs they care about most.

“If you’re a progressive that cares about investments in Head Start and student loan programs and medical research and infrastructure, we’re not going to be able to make progress on those areas if we haven’t gotten our fiscal house in order,” he said.

What he didn’t say to them, but was implicit, was that no deal is possible without some give by the Democrats, and that the political costs of appearing inflexible — as he will paint the Republicans if they continue to resist — could be significant.

Democrats think Obama has given considerable ground in the negotiations aimed at ensuring a vote to raise the government’s borrowing power by early next month. Whatever hopes the White House once had for a clean vote on the debt ceiling evaporated long ago when congressional Republicans resisted.

Beyond that, the formulas the White House has embraced include far more in spending cuts than in tax increases. That is in line with what many experts have endorsed — $3 or so in spending cuts for each new $1 in revenue — as the kind of agreement that would put the country on a more sustainable fiscal path. But it is anathema to many Democrats.

The president’s advisers have kept their focus on political independents, who they think are sick of gridlock in Washington and willing to reward politicians who step outside pure partisanship to solve the country’s problems. Democratic strategists think Republicans have misplayed the debt-ceiling negotiations to the point that, almost no matter the outcome, Obama can claim the high ground.

Recognizing the fragile state of the talks, Obama was more conciliatory toward Boehner and other Republican negotiators on Monday than he was a couple of weeks ago, when he derided them as not taking their responsibilities seriously.

But he tried to set some bottom lines, lest the talks drag on and on.

First, he said he would oppose any short-term agreement to get past the early August deadline. Second, he insisted that Republicans will have to give ground on revenue.

“I do not see a path to a deal if they don’t budge — period,” he said. “I mean, if the basic proposition is ‘It’s my way or the highway,’ then we’re probably not going to get something done, because we’ve got divided government.”

Obama said Republicans and Democrats are living with the consequences of a polarized political environment that rewards politicians “for saying irresponsible things to win elections or to obtain short-term political gain.” That means, he added, that “when we actually are in a position to try to do something hard, we haven’t always laid the groundwork” to get it done.

Negotiators have vowed to meet daily until they reach an agreement. For Obama, the test now is whether he can turn his ambitious rhetoric into a workable compromise.