When Mitt Romney was governor, he had a routine: Every Monday afternoon at 3, he would meet with the two Democrats who controlled the Massachusetts legislature. They rotated offices each week and, over cheese, juice and popcorn, the three negotiated the budget, taxes and health care. Sometimes they just chitchatted about movies, leaving Romney to wonder whether he had just wasted an hour.

This was how Romney governed as a Republican here on Beacon Hill, where the legislature was 85 percent Democratic. He was practical, not ideological. He was polite and formal, even in his Cabinet meetings, and kept his guard up with those outside his tight circle of loyalists. He forged relationships based on respect, but rarely trust. He sought compromise whenever possible, knowing that he would accomplish nothing if he didn’t win support from the other side.

Romney achieved results with this approach, and he thinks he can do the same in Washington. On the campaign trail, he touts himself as a consensus builder — a leader in ways that he charges President Obama is not. Romney said he could have broken the stalemate in Congress over extending the payroll tax cut by summoning both parties’ leaders to the White House. And if they didn’t show up, he said, he would have ventured down Pennsylvania Avenue to their offices.

“A leader listens to the people who are one’s opponents — and you find ways of bringing people together,” Romney said this week while campaigning in New Hampshire. Being a GOP governor in Democratic Massachusetts, he added, “taught me I had to get along. I couldn’t attack the speaker of the House or the Senate president because I had to work with those guys to get anything done.”

This a risky proposition from anyone seeking to be the standard-bearer of today’s Republican Party, many of whose voters hunger for leaders willing to blow the place up rather than compromise. And it is especially risky for Romney, whose evolution on key issues has left many in his party suspicious of his avowed conservatism. It could, however, help him woo independent voters in a general election.

“If Romney is elected, given the position of the Republican Party in the House and the Senate, where the energy of the party is and where the broad sentiment is, if he tried to start cutting deals with Democrats, Romney would find himself without a party,” said Thomas E. Mann, a congressional historian at the Brookings Institution.

The choice for Republican voters as they begin selecting a nominee in a little over a week is between a pragmatist and more of a blow-up artist. Whom they choose will make a big statement about the future of the GOP. If they pick Romney, will Republicans be satisfied with a pragmatist, given the hard ideological currents coursing through the party’s base? If they pick a partisan warrior — former House speaker Newt Gingrich or a host of other hopefuls — will the GOP be able to withstand the collateral damage that could come?

And would either type of president be able to break the dysfunction that has seized Washington?

‘I will respect people’

When Romney became governor in 2003, his brand of fix-whatever’s-broken bipartisanship was in vogue. He quickly closed a $3 billion budget deficit and, in 2006, earned national acclaim by signing a landmark bill that extended health-care coverage to every­one. Romney achieved both with significant support from Democratic lawmakers.

Romney regularly contrasts Obama’s toxic relationship with congressional Republicans with what he casts as a good working relationship between him and Massachusetts Democrats.

At an Iowa town hall meeting last month, a woman told Romney she was “tired of people blaming everybody else” and asked him what he would do to “actually get stuff done.”

Romney cited his Massachusetts experience and added: “We have to return to a time in Washington where Republicans and Democrats are able to work with each other. I will respect people across the aisle. Democrats love America, too. And even though we have differing views on issues, we can find common ground.”

Obama, too, campaigned for the White House pledging to bridge partisan divides, but he has been unable to fulfill those promises.

Romney says that’s because Obama “doesn’t know how to lead.” But some congressional watchers doubt Romney could, either, given that Congress is likely to remain bitterly divided regardless of whether Republicans keep control of the House and win back the Senate majority. If House Speaker John A. Boehner (R-Ohio) can’t steer his opinionated GOP conference toward deals on the big issues, how could Romney?

“It’s as naive as Obama’s post-partisan politics promises,” Mann said of Romney’s common-ground message. “It’s just a complete mishmash.”

Adjusting to politics

After winning the governorship in 2002, Romney, ever the management consultant, took to a giant white board to sketch out how the state government was organized. He appointed Bob White, an old friend and fellow partner at the private equity firm Bain Capital, to assemble a Cabinet. As his chief of staff, Romney picked Beth Myers, a lawyer who played his Democratic opponent, Shannon O’Brien, in debate rehearsals.

Before his inauguration, Romney brought together his top appointees and senior staff for a breakfast at the Parker House, the noted Boston hotel, to outline how he wanted his administration to behave. Romney wanted his staff to debate vigorously, but only in private.

“Mitt is very good at playing the devil’s advocate,” White said. “It wasn’t just necessarily important what your answer was, but he was trying to understand the depth of your thinking to get to that answer.”

Romney also ordered his administration never to unleash ad hominem attacks on political opponents. “I didn’t attack my legislature,” Romney said this summer in New Hampshire. “I didn’t go out and say they’re a bunch of Neanderthals or whatever word you might use to denigrate people.”

Once Romney settled into his office, the capital’s transactional, relationship-based culture seem­ed foreign.

Robert E. Travaglini, then the Senate president, said of Romney: “He was a venture capitalist, he was very successful, he had been in a position of power and authority where his word usually was the deciding word. Now he was going to have to become part of a collaborative.

“To his credit, he made the adjustment,” Travaglini said. “He understood that friendships were important, that inclusion and courtesies and notifications were part of the daily routine.”

As negotiations over the health-care bill dragged on, Romney showed up unannounced at Travaglini’s East Boston home one Sunday morning to encourage him to “keep the faith and get it done,” Travaglini said.

This was one of Romney’s go-to techniques of connecting and persuading. Myers said Romney routinely would wander around Beacon Hill, popping in on mid-level and low-level staffers unannounced — ostensibly to say hello, but really to see for himself what they were up to.

But around rank-and-file Democrats, Romney was standoffish. Romney stood out as unusually worldly, well educated and traveled, and high-achieving. Democratic lawmakers and party leaders said they saw in Romney’s distant coolness and formality a looking down on those who made their careers on Beacon Hill.

“I don’t think he really had much use for politicians,” said Phil Johnston, who chaired the state Democratic Party at the time. “He just felt they were there to get in the way.”

Johnston added: “He was not an easy person to know. His staff kept him in a bubble. He wasn’t particularly accessible to the media or to the legislators — or to anyone, really. When he would go to an event, he’d come in with his SUV, go to the podium and give his statement, and get out.”

At the beginning of his tenure, Romney, grappling with the budget deficit, went to his first meeting with the state’s mayors to deliver bad news. He was seeking authority from the legislature to cut the amount of state money that flowed into cities and towns.

“He goes and delivers the message,” recalled Cindy Gillespie, one of his senior administration officials. “He is not somebody that turns to staff and says, ‘Okay, you go tell them.’ ”

The legislature gave Romney the authority he sought, and he made the cuts, helping to balance the budget.

Two years into his governorship, Romney printed a flier to voters touting his top 10 accomplishments. “On the cover, I had my picture — after all, I paid for this brochure and stuffed it in the Boston Globe,” Romney said. “But I also had a picture of the Senate president and speaker of the House, because they also helped achieve those things.”