House Republicans approved a budget on Friday that would fundamentally alter Medicare and Medicaid, lower taxes on individuals and corporations and cut $4.4 trillion from the nation’s deficit over the next decade.

With its passing, Republicans have officially put forth their vision for reducing the nation’s debt and defining how the federal government fits into people’s lives. It’s a sharply different approach from the one outlined by President Obama on Wednesday, setting up months of clashes between the two parties over a number of critical fiscal issues.

The first round of that battle will come in town hall meetings across the country over the next two weeks, as congressmen head home for an extended recess.

House Republicans are betting that Americans are so concerned about the nation’s mounting debt that they will respond to a bold plan to fix it, even if that prescription includes major changes to Medicare and other entitlements that most people support.

“This is our defining moment. We must choose this path to prosperity,” Budget Chairman Paul Ryan (R-Wis.), chief architect of the plan, said as two days of debate wound down.

Ryan’s budget, titled “The Path to Prosperity,” would spend about $40 trillion over the next decade — $6.2 trillion less than the budget President Obama proposed in February. The bulk of the savings would come from federal health-care programs, starting with a repeal of Obama’s ambitious new initiative to expand coverage for the uninsured.

Starting in 2022, Ryan also would end Medicare as an open-ended entitlement for new retirees and begin slowly raising the age of eligibility from 65 to 67. Instead of getting government-paid benefits, retirees could choose a private policy on a newly established Medicare exchange.

Medicaid would come in for even sharper cuts, exceeding $700 billion over the next decade. The GOP plan would end the financing partnership between the federal government and the states, replacing it with block grants that give states less money and free them to manage the program as they wish.

Tax cuts for corporations and other tax reforms would reduce the overall savings of the plan to $4.4 trillion.

All but four Republicans voted for Ryan’s 2012 budget blueprint, and every Democrat present voted against it, for a final tally of 235 to 193.

The Ryan budget has virtually no chance of being enacted into law, considering that Democrats still control the Senate and Obama opposes much of it.

In an interview with the Associated Press Friday, Obama said the proposed changes to Medicare would create a “fundamentally different society than the one that we have now.” Obama offered his own framework for an alternative this week that would decrease the deficit in part by raising taxes on the wealthiest Americans and cutting military and domestic spending.

Nonetheless, the Ryan plan could prove useful to Republicans as they enter a season of protracted negotiations over spending issues with the president and his Senate allies.

Republicans intend to use pieces of the budget as bargaining chips in reaching a deal to increase the federal government’s ability to borrow money. And in the fall, Ryan’s budget will serve as the framework for setting 2012 spending levels for federal agencies.

Democrats believe Republicans made a political mistake in embracing the Ryan budget. They think it gives House Democrats, who had been largely irrelevant for the first 100 days of their minority status, a chance to regain traction with seniors -- a critical voting bloc that swung by 21 points in the GOP’s favor in the 2010 midterms.

“I want to say to my Republican colleagues: do you realize that your leadership is asking you to cast a vote today to abolish Medicare as we know it?” Minority Leader Nancy Pelosi (D-Calif.) said from the House floor during Friday’s debate.

On the eve of Friday’s budget vote, the Democrats’ top political architect was giddy at the thought of the dozens of Republican freshmen in elderly-heavy districts in Florida, Pennsylvania, Ohio, Illinois and Michigan voting for the plan.

“Go for it,” said Rep. Steve Israel (N.Y.), chairman of the Democratic Congressional Campaign Committee. “We will hold them accountable for making that choice.”

Not a single Republican from a swing district — 14 of them hold seats that Obama won in 2008 and Sen. John Kerry (D-Mass.) won in 2004 — voted against the Republican budget.

Changing Medicare has long been one of the riskiest bets in American politics. Upon winning a congressional majority in 1994, Republicans pushed a budget-balancing plan that sought $270 billion in Medicare savings, only to be out maneuvered by then-President Clinton.

In 2010, with historically large majorities, Obama and congressional Democrats pushed through a health-care plan that drew more than $400 billion in savings from Medicare. That led to GOP charges of hurting seniors and the creation of “death panels” for the elderly.

Clinton easily won a second term in 1996 and Republicans seized the House majority in 2010.

Democrats are hoping to mount an aggressive campaign over the two-week recess, in which most lawmakers will be back home for the longest stretch since the 112th Congress began in early January. The DCCC is planning a radio campaign against dozens of freshmen, and the party hopes to use social media networks to connect with outside activists.

In a private meeting Thursday, Pelosi urged Democratic lawmakers to sound the alarm in their districts back home — through social media and YouTube and town hall meetings.

“Somebody got up and said, ‘What does a 500-pound canary say? Tweeeeeeet!’” Pelosi recounted in a brief interview, spreading her arms like a bird.

On Friday, Pelosi and other Democratic leaders exhorted a crowd of activists: “Hands off our Medicare!” they chanted.

Rep. Pat Meehan (R-Pa.), who won last fall in a moderate district in the Philadelphia suburbs, acknowledged the political danger in voting for Ryan’s budget. But he said he thinks voters would respect him for trying to fix the debt problem.

“There’s a political risk in all of this, but I think that there’s also a sense of resolve — that if we don’t start talking about it honestly, we’ll just continue to kick the can down into a situation that isn’t going to get any easier,” Meehan said.