Gehrke: What should we hope for from Sen. Mitt Romney? Maybe the next Hillary Clinton.

What do Hillary Clinton and Mitt Romney have in common?

Yeah, they both lost their bids for the presidency, twice, actually. And each once to Barack Obama.

But there’s more. In 2001, Clinton was the freshman senator from New York, branded by some a carpetbagger, with zero legislative experience and coming to the job amid a lot of questions.

How would she fit in in the Senate? Would her status as former first lady get her perks not usually afforded a junior senator — plum committee assignments or chairmanships? Would her elevated profile give her a pulpit to bash then-President George W. Bush?

What she did surprised a lot of people. She dug into the issues. She didn’t get the committees she wanted but she kept her head down, focused on New York issues and a legislative agenda, mostly stayed out of the headlines that first year and, well, acted like a freshman senator.

“Rather than becoming a Senate show horse, Clinton emerged as a Senate workhorse for the state of New York,” Sarah Binder, a senior fellow at the Brookings Institute, wrote after Clinton’s first year in office. “To her credit, she has taken up the serious business of attending to the interests of New Yorkers.”

Sen.-elect Romney finds himself in a similar situation and, as one D.C.-insider with ties to Team Romney told me, he expects Romney will respond similarly.

“I see Mitt being almost like Hillary Clinton, where he takes a step back, goes a little bit low-profile for a bit and really gets to know the Senate,” he said.

There are some indications he’s willing to put in the work. Look, for example, at his campaign. It would have been easy for Saint Mitt to file his paperwork, retire to his home in La Jolla for nine months, then show up tanned and rested to give an acceptance speech.

To his credit, he put himself out there — a lot more than he had to — hitting Republican Lincoln Day dinners and parades and greasy diners all over Utah. He even posted a little homage (or affront) to Johnny Cash’s “I’ve Been Everywhere” listing off his journeys.

The Clinton analogy only goes so far though. Unlike Clinton, this is not a resume-builder for Romney. Another run for president isn’t in the cards and he’s not worried about his next paycheck.

“I think he has a degree of independence that others may not enjoy,” said former Rep. Jason Chaffetz, who is close to the Romneys.

Chaffetz said the rigid seniority-based system in the Senate may frustrate someone who comes from a different background — in business, as governor and running the Salt Lake Olympics.

“He’s used to being the chief executive, not one of 100,” Chaffetz said.

Ignore any speculation he’ll get special treatment or plum committee assignments. Romney — who President Donald Trump either courted or tricked into being considered for secretary of state — wants to be involved in international and financial policy, so those are the committees he’s most likely to land.

But there are 100 egos in the Senate and no one willingly gives up prestige and power. He’ll have to pay his dues.

“He’s going to be at the bottom of the totem pole in terms of seniority on those committees, so there’s no fast-pass to a chairmanship,” said Boyd Matheson, the former chief of staff to Sen. Mike Lee.

And with Senate Majority Leader Mitch McConnell exerting tight control, Matheson said, legislative talent or knowledge of issues or a high profile don’t mean much.

“I think his biggest challenge is not going to be dealing with the president or the Democrats in the House. It’s going to be dealing with Mitch McConnell,” he said.

Romney will be pressured (he already has been) to be the designated Republican critic of Trump, to fill the vacuum left by the absence of Sens. Jeff Flake, Bob Corker and John McCain. Romney — who famously said of Trump in 2016 that he is “a phony, a fraud. His promises are as worthless as a degree from Trump University” — could easily play that part.

Don’t count on it, said Eric Fehrnstrom, who has been a Romney insider since the senator-elect’s days as governor of Massachusetts.

“Those who want him to be a constant thorn in the president’s side, I think, are going to be disappointed,” Fehrnstrom told Boston radio station WBUR last week. “He’s going to be his own person. He will speak up when he needs to and he’ll support the president when he thinks he’s doing the right thing.”

Romney was among the first Republicans last week to express the view that Robert Mueller’s investigation into Russian election meddling should be allowed to run its course. It’s those types of issues where he’ll use his prominence to take a stand.

“I have and will continue to speak out when the president says or does something which is divisive, racist, sexist, anti-immigrant, dishonest or destructive to democratic institutions,” Romney wrote over the summer.

But it does little good for a freshman senator to pick fights with the White House.

“There is sincere worry in Washington that he’s going to be pegged in that McCain-Flake category, which would inhibit his ability to get anything done,” Chaffetz said. “This president keeps score.”

More fundamentally, there is not a huge amount of policy daylight between Trump and Romney. They agree on issues like tax cuts; Romney has said he is more of a hard-liner than Trump on immigration; they agree on eliminating government regulations and a host of other issues.

So what do we expect from Mitt? Look for him to keep his head down and his mouth shut, to pay his dues, to send a message to voters by prioritizing Utah issues out of the gate — to make an effort to be a workhorse, not a show horse. In short, to follow the Clinton model. He could do a lot worse.