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Gov. Bobby Jindal:Mr. Jindal, 41, has a multifaceted appeal: His parents emigrated from India, which could draw the attention of Asian-American voters who have replaced Hispanics as the fastest-growing segment of the electorate. And Mr. Jindal can claim progress in reducing the growth in government spending during his five years as governor of Louisiana.

Though not a captivating speaker, he also enjoys strong support from tea partiers and GOP regulars.

He is considered an intellectual and philosophical conservative and cut his teeth running Louisiana’s Department of Health and Hospitals at the age of 24. But some who have been in their presence say he and Mr. Romney have not clicked the way Mr. Romney and Mr. Portman have.

Gov. Chris Christie: The voluble New Jersey governor, 49, was a constant campaigner for Mr. Romney in the primaries, and in the New Jersey capital of Trenton, he has used his line-item veto power to cut state spending despite Democratic control of the state Legislature. He also pushed through a measure this month making it easier to fire incompetent public-school teachers and harder for teachers to win tenure.

Earlier this year, he aligned with religious conservatives by vetoing the legalization of same-sex marriage.

But he offends many on the right by supporting a “path to citizenship” for illegal immigrants and some gun-control measures.

Gov. Scott Walker: The first-term governor, 45, is a hero to fiscal conservatives for winning passage of a limit on public employees unions’ collective-bargaining powers in Wisconsin. When Democrats and the unions tried to oust him in retaliation earlier this year, Mr. Walker won by an even bigger margin than his 2010 election, becoming the first governor of any party to survive a recall election.

From a Midwestern swing state, he is an evangelical Christian recently handed a speaking slot at the GOP nominating convention in Tampa, Fla., diminishing the likelihood of being tapped for the Romney ticket. He is said to be leery about leaving his post so soon after winning the hard-fought recall election.