When Rep. Paul Ryan delivers the Republican response to President Barack Obama’s State of the Union address Tuesday, many viewers will get their first look at a man whom GOP leaders are trusting to manage a central policy issue—how to cut the federal budget—that could shape the party’s image for years.

While unknown to most Americans, Mr. Ryan, 40 years old, has established himself as a leading conservative thinker on federal spending, shaped in part by his early work for supply-side icon Jack Kemp.

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Bloomberg NewsRep. Paul Ryan spoke on Jan. 6 about GOP promises to cut spending.

Now, Republicans not only have made Mr. Ryan chairman of the House Budget Committee, but on Tuesday the House is expected to vote to give him unprecedented powers to force spending cuts for the current fiscal year. That authority will allow Mr. Ryan to act unilaterally in setting an overall spending level for the rest of the year, a job usually handled by his full panel.

Hours later, Mr. Ryan will speak to the nation in a televised address following Mr. Obama’s remarks to a joint session of Congress. He was chosen for the role by House Speaker John Boehner and Senate GOP Leader Mitch McConnell.

In elevating Mr. Ryan, Republican leaders are taking what Democrats believe is a political risk. He has written an anti-deficit plan that includes politically explosive ideas—replacing Medicare with vouchers and allowing some workers to invest Social Security taxes in private accounts—that go beyond what even many Republicans are prepared to embrace.

But conservatives counter that the 2010 election outcome showed he is precisely the kind of political figure to put forth as the face of the Republican Party.

“If I was starting a football team in a national budget league, I’d pick Paul Ryan as the captain and quarterback,” said Rep. Dan Lungren (R., Calif.), an ally of the late Mr. Kemp. “There’s nobody in this House who’s taken as serious a long-term view on the budget as Paul Ryan.”

Democrats delight in spotlighting his controversial proposals and daring other Republicans to embrace them.

“Up until this point, the Republican leadership has been vague about what federal programs they want to cut,” said Sen. Bernie Sanders, a Vermont independent who caucuses with Democrats. “On the other hand, Congressman Ryan has been very clear on this subject.”

Delivering the party’s response to the president is an honor but by no means a ticket to stardom. Most such addresses aren’t memorable, though Louisiana Gov. Bobby Jindal drew wide attention in 2009, when his response to Mr. Obama’s first address to Congress was widely panned.

In Washington, Mr. Ryan’s speech will be closely watched not only because of his central role in the fight over federal spending. He also is seen as having higher political ambitions: Mr. Ryan is considered a possible candidate for the Senate in 2012 if Wisconsin Democrat Herb Kohl doesn’t run for re-election.

For now, Mr. Ryan’s platform is the hearing room of the House Budget Committee, from which he will broadcast his remarks Tuesday night. Republicans picked the venue to help draw a sharp contrast with Mr. Obama, who is expected to argue both for deficit reduction and for new government spending in areas such as education and infrastructure that he considers “investments” in economic growth.

In the past year, Mr. Ryan has gone toe-to-toe with Mr. Obama in high-profile venues. When the president a year ago addressed a conference of House Republicans in Baltimore, he called attention to Mr. Ryan’s “roadmap” and jousted with him over the plan’s details and implications. A month later, at a televised bipartisan summit on Mr. Obama’s health-care legislation, Mr. Ryan delivered a stinging critique of the bill to the president’s face.

At a time when his party has been swept to power in the House by anti-Washington feelings and the tea party, Mr. Ryan is an intellectual who has spent scant time working outside the Washington Beltway. He supported the Wall Street bailout that was a big spark behind the tea-party rebellion.

Born in Janesville, Wis., Mr. Ryan went straight to Capitol Hill after college to work on the staff of his home-state senator, Republican Bob Kasten. After Mr. Kasten lost his re-election bid in 1992, Mr. Ryan went to work at Empower America, a Washington think tank, where he wrote speeches for Mr. Kemp and conservative thinker Bill Bennett.

He worked as a marketing consultant for his family earth-moving business for a couple of years, then returned to Capitol Hill to work for conservative Sam Brownback, who at the time was in the House.

Mr. Ryan, who won an open seat in Congress in 1998, lives in his hometown with his wife, Janna, and three young children. When asked about speculation that he may run for president, Mr. Ryan has been known to respond: “My head isn’t big enough, and my kids are too small.”

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