With the selection of Rep. Paul Ryan (R-Wis.) as his running mate, GOP presidential candidate Mitt Romney has reframed the campaign as a choice of political philosophies — one in which Ryan’s controversial budget plan will be a flash point.

Romney had until now portrayed the race primarily as a referendum on the policies and the performance of President Obama. But his pick of the House Budget Committee chairman turns more focus on how Romney himself would govern — and if he wins, potentially provides a mandate for his presidency.

The budgets that Ryan has written have achieved a status close to dogma among conservatives, calling for a dramatic reordering of fiscal priorities and the scope of government. Democrats, meanwhile, believe the Ryan plan is a major liability for Republicans by alienating elderly and moderate voters.

His proposals contain three major elements:

First, the Ryan plan would overhaul the entitlement programs that have grown to consume about 40 percent of the budget, reshaping Medicare coverage for the elderly, and cutting deeply into Medicaid, food stamps and other programs for the poor.

Second, he would rewrite the tax code, slashing the rates paid by corporations and the wealthy.

Finally, Ryan would cut spending on other federal programs and agencies, with the exception of the Pentagon.

Most controversial is Ryan’s proposal to transform Medicare so that the government, rather than paying for health care for the elderly directly, would give beneficiaries a set amount of money to shop for a private health insurance plan.

Last year, working with Democratic Sen. Ron Wyden of Oregon, Ryan tweaked the idea to add an option in which the elderly could remain in the traditional Medicare program, but they would have to pay significantly more for that coverage if it turns out to be more expensive than private plans.

The politics of dealing with entitlements for the elderly have long been treacherous. That is why senior Republicans — while hailing Ryan for fresh, bold and creative thinking — initially maintained some distance from the particulars of the plan he first put forward in 2009, when he was the budget committee’s ranking Republican in a chamber controlled by the Democrats.

When the Washington Post-ABC News poll asked last year whether respondents would favor changing the Medicare program along the lines of the Ryan-written House budget, opinion tilted sharply negative. Only 32 percent supported it, while 49 percent were opposed.

As recently as last year, former House speaker Newt Gingrich, launching his own bid for the 2012 GOP presidential nomination, branded the Ryan budget “right-wing social engineering.”

Gingrich quickly apologized in the face of a backlash by conservatives, among whom Ryan had become a hero. Ryan’s ideas have become so dominant within the House that when his fiscal 2013 budget was put to a vote in March, only 10 Republicans opposed it.

On Saturday, shortly after Ryan’s selection was announced, Gingrich issued a statement hailing it as “a courageous choice for a BIG solutions election. Paul Ryan is the largest step the GOP has taken towards solving the country’s problems since [former President Ronald] Reagan and [former Rep. Jack] Kemp,” both icons of the tax-cutting “supply side” school of economics.

Romney did not give a full-throated endorsement to the Ryan plan until March, shortly before he locked up the nomination.

The federal budget deficit edges out jobs as the No. 1 economic issue among Republican voters in a new survey by The Washington Post and the Kaiser Family Foundation. Independents tend to be more focused on the employment situation, and for Democrats the deficit slides to third place as a main economic problem, behind jobs and the cost of health care.

Ryan’s proposal is one of three major approaches to deficit reduction that have dominated the discussion in Washington over the past few years.

The other two have been Obama’s own budget, and the recommendations of the bipartisan Simpson-Bowles Commission.

The White House budget would spend nearly $5.3 trillion more than Ryan over 10 years, mostly on health care and entitlements for the poor; it would also raise taxes on the wealthy, while Ryan would cut them.

Ryan had been a member of the Simpson-Bowles commission, but voted against its final recommendations, complaining it had not done enough toward bringing health care entitlement spending under control. The commission’s proposal also included $2 trillion in new taxes and $800 billion in defense cuts.

Beyond his proposal to revamp Medicare, the Ryan budget would transform other entitlement programs as well. It would cut spending on major programs for the poor, including Medicaid and food stamps, and give states more flexibility in managing them. Ryan would also impose time limits and work requirements on some programs, including food stamps, as he notes the 1996 welfare reform law did with cash payments.

Ryan supports a permanent extension of the Bush-era tax cuts, as does Romney.

Where there are currently six individual income-tax brackets, ranging from 10 percent to 35 percent, Ryan would streamline that to two brackets: 10 percent for low-income people and 25 percent for upper-income earners. His plan also calls for eliminating tax loopholes, but does not specify which ones should go.

Ryan would cut the corporate income tax, currently 35 percent, to 25 percent.

The Ryan budget’s bottom line, however, is not as rosy as some conservatives would like. The Congressional Budget Office estimates that it would not bring the federal books into balance until around 2040.

And most of its savings come from the long-term restructuring of entitlement programs. In the near run, it would add to the debt — by $3.1 trillion — between now and 2022, according to the House Budget Committee’s own projection.

Partisans on both sides say that Ryan’s selection has the potential to refocus a presidential race that had descended into a barrage of unsubstantiated accusations and negative advertising.

“This is now going to be about policy, and that is good for Republicans,” said David Winston, a pollster who advises the House GOP leadership. “If you win by a good margin, and it’s clear what you were running on, then you come into the presidency with an ability to implement those policies.”

But the move also opened a new line of attack for Democrats, with the Ryan-authored House GOP budgets offering a far more detailed set of proposals than Romney himself has put forward.

“This choice demonstrates that Mitt Romney is doubling down on an economic agenda that benefits people like Mitt Romney at the expense of the rest of the country,” said Rep. Chris Van Hollen (D-Md.), who as the ranking Democrat on the House Budget Committee is a frequent foil to Ryan. “It will clearly sharpen the issues.”

Lori Montgomery and Jon Cohen contributed to this report.