In late 2004, a meeting of House Republicans grew heated as they discussed whether to change their rules and allow Majority Leader Tom DeLay to stay in the leadership even if he were indicted in a Texas corruption probe.

It was Rep. Rob Portman (Ohio) who offered the compromise that settled the matter: A committee controlled by party leaders should decide DeLay’s fate, Portman said, according to several participants.

“It was typical Rob, trying to find a thoughtful way forward that solves the problem but doesn’t overreact,’’ said former congressman Tom Davis (R-Va.).

Supporters say that is a critical asset for Portman, now a first-term senator and considered to be among the leading contenders for Mitt Romney’s vice presidential running mate.

But Democrats see it as a way to tie Portman to DeLay, who was later convicted of corruption in the Texas probe. And the episode points to a potentially broader vulnerability if Portman were selected: his longtime status as a Washington insider — and the baggage that can go with that — when Romney is running as an outsider.

Portman, who spent Monday addressing Romney supporters in Ohio, continues to draw attention as a potential No. 2 on the GOP ticket. He is respected by both Democrats and Republicans as savvy and cerebral. And Portman, 56, could help Romney in Ohio, a crucial swing state.

His two decades of Washington experience includes a stint at the D.C. lobbying powerhouse Patton Boggs, where he registered as a foreign agent and advocated for Duty Free Shoppers, a Hong Kong-based operator of airport and other duty-free stores. The company has had a web of offshore affiliations, records show, including incorporations in Bermuda and the Netherlands Antilles, often used as tax havens.

While he was in Congress, Portman’s PAC accepted $4,000 from Indian tribes represented by D.C. superlobbyist Jack Abramoff — convicted in a scandal that came to symbolize Washington corruption — along with $500 from a convicted colleague of Abramoff. Records show that many Republicans, and some Democrats, accepted similar tribal donations.

A Portman aide said the senator has no recollection of meeting Abramoff. Portman’s office declined to comment on his vice presidential prospects or other aspects of his record.

Portman’s long-standing ties to the Bush family would probably be raised by President Obama’s campaign, which is trying to tie Romney to the Bush years. Portman served in President George H.W. Bush’s administration and then worked for President George W. Bush as U.S. trade representative and budget director. Former Bush aides say he consistently pushed to rein in spending and convinced others in the White House to propose a balanced budget.

Portman “is a strong candidate, an experienced guy, with a deep understanding of the issues,’’ said Democratic strategist Tad Devine. But he “could undercut Romney on Washington insider. If he turns out not to be one member of Congress but also a lobbyist, a Bush White House staffer and he starts looking like Mr. Inside, it will look like Romney will be just the same old, same old.’’

The Obama and Romney campaigns declined to comment. Earlier this year, Portman told Ohio-based reporters that he was “proud” of his service as Bush’s budget director and contrasted his record with that of Obama, who he said has presided over the weakest economic recovery “since the Great Depression.’’

Former House speaker J. Dennis Hastert (R-Ill.) praised Portman as “a great public servant” who always kept his home in Ohio and “didn’t let Washington go to his head. . . . They don’t have a lot of stuff to hang on him.’’

Portman, a Cincinnati native, grew up working for the family’s Portman Equipment Co., a forklift truck dealership. His congressional disclosure forms show income from the business has contributed to his net worth, estimated at between $6 million and $22 million.

In 1984, fresh out of the University of Michigan law school, Portman began working as a lawyer at what was then Patton, Boggs & Blow. Federal records show he registered in 1985 under the Foreign Agents Registration Act, which requires U.S. firms to disclose contracts to represent the interests of foreign governments or entities.

Portman’s registration lists the governments of Haiti and Oman as possible clients, but a Patton Boggs partner said Portman never worked on those accounts. He did spend as much as 15 percent of his time working for Duty Free Shoppers, the partner said. Government records show he lunched twice with a congressional staffer on the company’s behalf.

Although Portman was part of a team that lobbied government officials extensively on behalf of the duty-free-retailing industry, a Patton Boggs official and a person close to Portman said he did not lobby but rather attended meetings as a lawyer with expertise in trade issues.

“He was not in any classic or normal sense a lobbyist,’’ said Stuart M. Pape, a Patton Boggs partner who supervised Portman.

A spokeswoman for Duty Free Shoppers, now called DFS, declined to comment. The company’s offshore affiliations could play into Democratic efforts to target Romney for his former private-equity firm’s investments in companies that specialized in helping other firms relocate work overseas. Republicans warned that such a tactic would backfire.

“This goes back 30 years. President Obama was doing cocaine 30 years ago,’’ said John Feehery, a Republican consultant, referring to Obama’s admitted drug use in high school and college. “If they want to play that game, they need to be careful.’’

Portman served in the House from 1993 until he left to join the Bush administration in 2005. Former colleagues say he was not close to DeLay and had received Hastert’s blessing before proposing the November 2004 compromise that meant DeLay might not have to step down if indicted.

After an outcry from good-government groups and some Republicans, the party restored the old rule requiring leaders to step down if indicted, and DeLay stepped aside when he was charged in 2005. He was convicted in 2010 of illegally plotting to funnel corporate contributions to Texas legislative candidates and sentenced to three years in prison.

Like many Republicans, Portman strongly defended DeLay, telling The Washington Post in 2004: “People are grateful for what he’s done,’’ including DeLay’s efforts to promote Republican interests in Texas.