Rep. Paul Ryan of Wisconsin accepted the GOP nomination for vice president on Wednesday with a declaration that President Obama, who was elected four years ago on a promise of hope and change, has failed and his opportunity has been squandered.

Ryan told delegates gathered at the Republican National Convention here that Obama’s presidency is “adrift, surviving on slogans that already seem tired, grasping at a moment that has already passed.”

Ryan’s selection was a big gamble for presidential candidate Mitt Romney, given the House Budget Committee chairman’s authorship of a controversial budget that would overhaul the federal Medicare program — whose preservation is an issue on which Democrats have frequently bested Republicans.

“Our opponents can consider themselves on notice,” Ryan said. “In this election, on this issue, the usual posturing on the left isn’t going to work. Mitt Romney and I know the difference between protecting a program and raiding it. Ladies and gentlemen, our nation needs this debate. We want this debate. We will win this debate.”

Ryan’s nomination will put more pressure on the Republican ticket to articulate and defend its economic vision, rather than simply stoking the electorate’s disappointment and dissatisfaction with Obama. Ryan, however, stuck to broad themes rather than gritty specifics in a speech that marked the first time many Americans have seen and heard the vice presidential nominee.

Again and again, delegates rose to their feet and cheered as Ryan warmed to the traditional running mate’s role as aggressor. Scott Walker, his home-state governor and longtime friend, wept.

“I have never seen opponents so silent about their record and so desperate to keep their power,” Ryan said. “They’ve run out of ideas. Their moment came and went. Fear and division are all they’ve got left.”

However, at several points, Ryan critiqued Obama’s positions without disclosing the fact that he had held similar ones. For instance, although he attacked Obama for reducing Medicare spending by more than $700 billion, his own budget proposal would curb the program by a similar amount. He also criticized the president for not supporting the recommendations of a bipartisan commission on deficit reduction, without noting that he had been a member of the commission and had not supported it either.

At 42, the congressman from Wisconsin is the first member of Generation X to run on a presidential ticket. He reflected his cohort’s anxiety that the Social Security and Medicare programs cannot be sustained long enough to take care of them in their retirement years.

“I accept the calling of my generation to give our children the America that was given to us, with opportunity for the young and security for the old — and I know that we are ready,” he told the delegates.

“I’m going to level with you,” he said. “We don’t have that much time. But if we are serious, and smart, and we lead, we can do this.”

When Ryan laid out his first major fiscal proposal three years ago, many in the upper ranks of the GOP were skittish about its particulars, especially the transformation of Medicare from a government-financed system to a voucher program.

Having passed the House twice since then, the Ryan budget represents the epicenter of conservative Republican philosophy, calling for a dramatic shift in government priorities and a sharp reduction in the scope of its mission.

But many of its individual provisions remain unpopular with the electorate at large, and Democrats have made it clear that they intend to make the Ryan budget a major element in their case against Romney.

The latest Washington Post-ABC News poll suggests that although Romney’s selection of Ryan did not change the basic dynamic of the campaign, it boosted Republicans’ excitement about their ticket.

Where Obama in previous polls held a double-digit lead on that measure, the candidates now are roughly equivalent in the amount of energy they are generating with their party ­bases. In the new survey, 48 percent of Obama supporters say they are “very enthusiastic” about his candidacy, compared with 42 percent of Romney’s.

Very conservative voters overwhelmingly approve of Ryan’s selection, and for the first time in this election cycle, their enthusiasm rivals that of liberals for Obama.

To Republicans on the right, who have long been skeptical of Romney, his selection of Ryan sent a strong message.

“It said: This guy’s got the courage and the passion to be an exceptional president,” Walker said at a breakfast Wednesday with journalists from The Washington Post and Bloomberg News. “He said: This is a guy who’s got the guts to put someone like Paul Ryan on the ticket, who’s actually willing to govern like he’s campaigning.”

Obama’s campaign, however, contends that the Republican ticket has tried to gloss over the pain that would be inflicted by the spending cuts and entitlement changes in the Ryan plan. It also said the tax cuts that the plan envisions would worsen the nation’s fiscal situation.

In criticizing Ryan, Obama campaign aides — some of whom were making the rounds at the convention center in Tampa — echoed an argument that New Jersey Gov. Chris Christie had made against the president in his keynote address the night before.

“We heard a lot of talking [Tuesday night] about tough choices and hard truths,” Obama campaign spokesman Ben LaBolt said. “The burden on them is to explain why tax cuts weighted to the wealthiest would work.”

One speaker who tried to rebut that contention was Sen. Rand Paul (Ky.) — the son of Rep. Ron Paul (Tex.), who sought the nomination this year and in 2008.

Rand Paul, a tea party favorite who won his Senate seat after defeating the GOP establishment in his state, offered a vigorous defense against Obama’s contention that the wealthy and corporations should bear more of the tax burden.

“Mr. President, you say the rich must pay their fair share. But when you seek to punish the rich, the jobs that are lost are those of the poor and middle-class,” Paul said.

Wednesday’s convention proceeding touched a number of political bases.

Former Arkansas governor Mike Huckabee, who competed against Romney for the GOP nomination in 2008 (both fell short), argued that his fellow evangelical Christians should get over their leeriness of Romney’s Mormon faith.

“I care less about where Mitt Romney takes his family to church than I do about where he takes this country,” Huckabee said.

Former secretary of state Condoleezza Rice, the only high-profile member of the George W. Bush administration to have a prominent role at the gathering, gave what was one of the most stirring speeches of the convention.

She recalled her upbringing in the segregated South and lauded the parents who could make that little girl “believe that even though she can’t have a hamburger at the Woolworths lunch counter, she can be president of the United States and she becomes the secretary of state. America has a way of making the impossible seem inevitable in retrospect. But of course it has never been inevitable — it has taken leadership, courage and an unwavering faith in our values.”

Rice went on: “Mitt Romney and Paul Ryan have the experience and the integrity and the vision to lead us — they know who we are, what we want to be and what we offer the world.”

For the first time during the convention, foreign policy took the spotlight alongside domestic economic issues.

Rice obliquely criticized Obama’s international approach.

“The promise of the Arab Spring is engulfed in uncertainty; internal strife and hostile neighbors are challenging the fragile democracy in Iraq. Dictators in Iran and Syria butcher their own people and threaten the security of the region. China and Russia prevent a response, and all wonder, ‘Where does America stand?’ ” she said. “When our friends and our foes alike do not know the answer to that question — clearly and unambiguously — the world is a chaotic and dangerous place.”

Aaron Blake and Jon Cohen in Tampa and Karen DeYoung in Washington contributed to this report.