WASHINGTON — He has played the role of Hillary Rodham Clinton, Al Gore and Barack Obama. He has spent hours studying intricate details of their policy positions, perfecting the cadences of their voices and refining the lines of attack against their Republican opponents.


For more than a decade, Senator Rob Portman, Republican of Ohio, has deployed an unusual expertise: impersonating Democrats to help candidates in his own party prepare for debates. He has frustrated George W. Bush, agitated Dick Cheney and pushed John McCain beyond the brink of irritation.


“I hate him still,” Mr. McCain said with an admiring air of sarcasm, laughing in a brief interview as he recalled their testy practice sessions four years ago. “Because he’s such a jerk, he gets under your skin, says things that are impossible to respond to.”


But this year, Mitt Romney may have another part in mind for Mr. Portman.


The search for Mr. Romney’s running mate is entering its final phase, and Mr. Portman, who has ascended to senator from staff member during nearly three decades in Washington, is believed to be high on the list of prospects. He has campaigned repeatedly with Mr. Romney, and he is flying to New Hampshire this week — where the Romney family is vacationing — to appear at a Republican fund-raiser.


Mr. Portman, who was elected to the Senate in 2010 after representing the Cincinnati area in the House for 12 years, is relatively unknown to most Republicans across the country. But here in Washington, where he worked in both Bush administrations and has won praise as an effective legislator, he is among a select breed of politicians who have a keen and deep understanding of the inner workings of government.


When he arrived in the Senate, he startled some Republican colleagues when he pulled out his own charts and graphs that analyzed the nation’s rising deficits and its debt of $15 trillion. His earnestness initially rubbed a few people the wrong way, particularly because of his tenure as budget director for President George W. Bush.


At a time when fiscal concerns weigh heavily on the electorate, and the tug of war between the Republican establishment and the Tea Party still simmers, many conservatives still blame Mr. Bush and his team for allowing increases in government spending and budget deficits that they consider excessive. In interviews, several friends argued that since Mr. Portman served for only a year as director of the Office of Management and Budget, he did not bear responsibility for the administration’s full record.


If Mr. Romney is looking for a stirring orator to help electrify the ticket, Mr. Portman may not be his first choice. But for a governing partner with strong relationships in Congress, Republicans believe Mr. Portman is far more attractive.


The vetting of possible vice-presidential candidates has been under way for months. It is a deeply secretive process overseen at the Romney campaign headquarters by one of the candidate’s most trusted confidantes, Beth Myers. Last month, Mr. Romney tried to discourage speculation by declaring, “There are only two people in this country who know who are being vetted and who are not.”


Republicans close to Mr. Romney believe Mr. Portman is on the list, along with a handful of others including former Gov. Tim Pawlenty of Minnesota, Representative Paul D. Ryan of Wisconsin and Gov. Bobby Jindal of Louisiana. The roster could be larger, associates of Mr. Romney caution, but many Republicans argue that Mr. Portman is ideally suited for campaigning in Ohio and other critical Midwestern states.


“He would probably be the best-prepared person of anyone since George Herbert Walker Bush became Ronald Reagan’s vice president,” said Joe Hagin, who also worked in both Bush administrations and has known Mr. Portman since childhood. “He has an immense understanding of the budget, the tax code and trade and foreign policy.”


Mr. Portman, 56, has close ties to the Bush family. Barbara Bush recorded radio advertisements that helped him win an early Ohio Congressional race. This week in Maine, Mr. Portman is scheduled to have lunch with the elder George Bush, whom he served in the White House as associate counsel and head of legislative affairs.