Day Two of Donald Trump’s presidential transition brought the president-elect and his running mate Mike Pence to Capitol Hill. It’s almost certain to be a frequent haunt for the former six-term congressman and current governor of Indiana.

Trump and Pence both sat down with House Speaker Paul D. Ryan and Senate Majority Leader Mitch McConnell on Thursday afternoon, in the leaders’ first face-to-face meeting since Trump’s stunning win on Tuesday.

Trump is the first president to enter the White House without any governing experience. So Republicans on Capitol Hill are looking to Pence to serve as his de facto sherpa in congressional matters.

Pence not only served in Congress from 2001 to 2013, but he also led the Republican Study Committee, a group of conservative House members, and rose to become GOP conference chairman. He and former Speaker Newt Gingrich could be familiar faces within an administration that was propelled to power by vows to shatter the old order in Washington. 

“We all really like Mike Pence,” McConnell said Wednesday.

The Kentucky Republican recalled former Vice President Dick Cheney’s frequent appearances at Senate Republicans’ Tuesday policy lunches as a potential model for Pence.

“I mentioned that to Vice President Pence,” McConnell said, “and I hope he will attend our Tuesday policy lunches when he’s in town and kind of be our liaison between the administration and the Senate, much like Vice President Cheney was.”

Pence has previously pointed to Cheney as someone he would like to emulate. When Pence met with House and Senate Republicans in mid-September, he discussed his potential role as an involved vice president. 

“There were a lot of nodding heads,” recalled Indiana GOP Sen. Dan Coats. “That’s really what we need and really what we have missed. … He just said he wanted to be very, very active.”

It would not be unusual for Pence to have an influential role in the Trump administration, said Joel K. Goldstein, a law professor at St. Louis University who studies the vice presidency.

“I think beginning with [Democratic Vice President Walter] Mondale, the vice presidency has really taken on sort of a continuing role of a senior adviser and troubleshooter for the president,” Goldstein said.

The vice presidency used to be looked down upon as an ineffective position, but recent vice presidents have served as influential confidants. Trump’s lack of governing experience especially positions Pence to take that role, Goldstein said.

That, of course, depends on how much Trump wants to delegate and how much he listens to his second in command.

It’s still a question whether Trump would be comfortable with Pence taking a leading role in working with Congress, especially since a number of lawmakers have said they would have preferred Pence as the GOP presidential nominee.

After the release last month of a 2005 video that showed Trump bragging about groping and kissing women, a number of congressional Republicans called on Trump to step aside and let Pence run at the top of the ticket. 

“Trump could see Pence as a competitor and resent the fact that some of them prefer Pence,” Goldstein said. “On the other hand, he could see Pence as someone who could help him deal with people who really are suspicious of him.”

Some of Pence’s allies on Capitol Hill said the latter possibility is more likely, and it’s clear Trump trusts his vice presidential pick.

“I think they have a very secure relationship with each other,” Alabama Republican Rep. Robert B. Aderholt said. “And I think Donald Trump trusts him tremendously in trying to reach out to whatever groups.

Aderholt has been close to Pence since they served together in the House. They were neighbors in Virginia and the Pence children were frequent babysitters for Aderholt’s younger children.

Pence’s personal ties with his former House colleagues (some of whom are now in the Senate) could prove valuable if there are intramural blow-ups over strategy or policies. Pence’s allies also said he can work with Democrats.

“Mike Pence has the demeanor and he has the personality that he doesn’t make people feel uncomfortable if they’re a different party,” said Aderholt.

Democrats sharply criticized Pence when he was chosen as Trump’s running mate, citing laws he promoted as governor that they said allowed for discrimination against lesbian, gay, bisexual and transgender Americans.

But Democrats are now saying they will approach the Trump administration with an open mind. Pence began reaching out to top Democrats on Thursday, speaking with New York Sen. Charles E. Schumer, likely the next Senate Democratic leader, according to a person familiar with the call.

Pence also phoned House Minority Leader Nancy Pelosi of California and the two “agreed on the need to find common ground,” according to a Pelosi spokesman. A Pelosi aide also said the two have a friendly relationship and their families have interacted at events over the years in Washington.