Under pressure from Republicans, President Obama offered a broad vision for solving the nation’s long-term fiscal problems Wednesday. This was not a speech about dollars and cents as much as it was an appeal for Americans to think about what kind of country they want and how they define shared sacrifice.

Obama’s address left many questions unanswered, but there was no doubt that the president and his White House advisers regarded it as one of the most important political speeches he will make in his second two years in office. It was an effort to regain the offensive in a debate that will dominate budget negotiations for the rest of this year and will probably shape the choices voters will face in the 2012 presidential election.

Obama appeared to have two goals in mind. First, he sought to demonstrate that he is serious about solving the debt and deficit problems that threaten the country’s fiscal future. Second, he needed to prove to Democrats that he is prepared to take on the Republicans and fight for policies that his party has long stood for.

The question is whether he can do both. The angry reaction from many Republicans suggests he may have widened the gulf between the two sides, although bipartisan talks in the Senate continue.

In the recent negotiations over funding the government for the rest of this fiscal year, Obama gave considerable ground, at least in the overall size of the spending cuts. His concessions alarmed many Democrats, who fear that he will continue to yield to the GOP in the future. Wednesday’s speech was an effort to say that there are lines he will not cross in the coming talks about raising the debt ceiling and about future budgets.

The president has been on the defensive for weeks in the budget debates, and his hand was called when House Budget Committee Chairman Paul Ryan (R-Wis.) announced his long-term fiscal blueprint last week. In responding, Obama laid down clear markers that established profound differences in governing philosophy.

Obama said the GOP proposal offers worthy goals for stabilizing the budget, but he took sharp exception to the path it would follow. “The way this plan achieves those goals would lead to a fundamentally different America than the one we’ve known, certainly in my lifetime,” he said. “In fact, I think it would be fundamentally different than what we’ve known throughout our history.”

Obama charged that the Republicans would threaten the social compact that long has governed society. What he hopes to prove is that that compact can be maintained while stabilizing the government’s fiscal condition. “To meet our fiscal challenge, we will need to make reforms.” he said. “We will all need to make sacrifices. But we do not have to sacrifice the America we believe in. And as long as I’m president, we won’t.”

By all the old rules of politics, Obama would appear to be on solid ground in many of his arguments. He said he will oppose Republican proposals to turn Medicaid into a block grant to the states and to sharply limit the amount of money the government spends on health care for poor people. He said he is against turning Medicare into a voucher program, as Ryan’s blueprint proposes, even though some Democratic deficit-reduction plans move somewhat in that direction.

Both of those stances have proved to be winning arguments in past political debates, but it’s not clear this time whether Obama has a real plan for saving enough money in Medicare to ensure its future financial solvency.

The president also called for cuts in the Pentagon budget, which Ryan’s plan would not touch.

His sharpest distinction with the Republicans came over taxes. Republicans insist that the deficit should be reduced without raising taxes. Obama renewed his call to raise taxes on the wealthiest Americans, drawing heavy criticism from the GOP.

Polls show strong support for taxing the rich, just as they show opposition to cutting Medicare. But despite a campaign pledge to raise tax rates on income above $250,000, Obama has been unsuccessful in doing so, even when Democrats had sizable majorities in the House and the Senate.

Obama hopes to prove that he can successfully run part of the old Democratic playbook while coming to terms with a fiscal problem that he agrees needs to be dealt with in a comprehensive way.

William Galston of the Brookings Institution recalled Wednesday that there was a big debate inside the White House in 1995 over whether President Bill Clinton should propose his own plan for balancing the budget to answer the Republicans’ proposal. Once he did, Galston said, thereby demonstrating that he and the Republicans differed over means and not ends, Clinton gained the upper hand politically. Obama may hope that his speech will accomplish the same thing.

Obama has long talked about the need to get serious about addressing the problem of debt, deficits and the size of government. But in his first two years in office, he did little to make good on that commitment. His adversaries say he has done just the opposite by running up record deficits, with projections of trillions in new debt over the next decade.

Although he appointed a commission to make recommendations for dealing with debts and deficits, the president appeared to keep the group at arm’s length. In his State of the Union address in January, he barely referred to its plan and then seemed to ask the Republicans to take the first step to engage — which they did.

He has been criticized repeatedly for remaining on the sidelines in the budget battles. The president’s advisers say he long has intended to give the kind of speech he delivered Wednesday but thought he needed to get the 2011 budget resolved before entering into a bigger debate.

Critics scoff at that explanation, wondering how that can be the case when the budget he just submitted to Congress falls far short of the goals he outlined. If he had been serious about engaging this debate, they say, he would have done more to highlight it earlier.

Last week’s agreement on the 2011 budget seems to have convinced Obama that the coming debate over raising the debt ceiling will not be easy and that he and the GOP will need to make some progress on at least a framework for dealing with long-term spending problems. His call for bipartisan negotiations to begin soon, with Vice President Biden representing the White House, underscores that recognition.

Few believe Democrats and Republicans can reach an overall agreement by June, as the president called for in his speech, which is why this debate is likely to carry well into next year. Obama knows that reaching an acceptable deal with the Republicans would allow him to claim that he had tamed the partisan beast in Washington. Absent such a bargain, Wednesday was all about laying the foundation for a grand debate between the president and his Republican challenger in 2012.