"I have the highest, highest regard for Mike. He's a personal friend of ours and mine," House Speaker Paul Ryan told reporters on Tuesday, adding that he would withhold any more comment until Trump announces his pick.
Pence served six terms in the House, and most recently was a top-ranking leader who handled political messaging for the GOP conference. However, before leaders added him to the leadership table, he was frequently a thorn in their side. As chair of the conservative Republican Study Committee, he pushed for deeper spending cuts, was an early supporter of getting rid of so-called "earmarks" and at times criticized fellow GOP members.
Pennsylvania GOP Sen. Pat Toomey, who faces a tough re-election race, weighed in favor of the Indiana Republican. "I'm a big fan of Mike Pence. I think he'd be a great choice," he said.
One House Republican who has been skeptical of Trump told CNN: "Pence would really help things with the party establishment."
Pence will appear with Trump Tuesday night at a campaign event in Westfield, Indiana, in an audition of sorts to be the billionaire's running mate. A person familiar with Trump's deliberations said Pence and former House Speaker Newt Gingrich appear to be the front-runners
in the process.
One reason why Republicans are more comfortable with Pence: They are nervous about other finalists on Trump's short list. Gingrich, while an effective debater, would undermine Trump's message as an outsider. And New Jersey Gov. Chris Christie has irritated many on the Hill with his antics, dating back to how he berated many Republicans for their handling of Hurricane Sandy aid money.
Arizona GOP Rep. Jeff Flake, a critic of Trump's who clashed with the businessman
at a meeting with Senate Republicans last week, echoed Toomey, saying he was "a big fan" of Pence and added, "I think he probably has a better chance of moving the candidate to where he maybe should be."
Rep. Cathy McMorris Rodgers, R-Washington, who served with Pence in the House leadership and now is in the post he held in the House as chair of the GOP conference, told CNN the talk about Pence was "exciting," adding, "we'll see how this all plays out. I think the fact that we all know him, we've all worked with him, there's a working relationship that would be there."
Republicans in both chambers noted that Pence's credentials as a reliable fiscal and social conservative.
"He's a conservative. He's an honest guy. He's a straightforward person," Utah Sen. Orrin Hatch told reporters, who also pushed back at some conservative commentators who questioned whether Pence was still conservative. "He's been a good governor in spite of some of the criticisms that have come down the pike. He's gutsy. I think he'd be fine," Hatch said.
But Pennsylvania Rep. Charlie Dent, who is among a dwindling group of moderate Republicans, said Pence has "a nice tone and a nice temperament, but in terms of broadening the appeal beyond the base, I don't know that his selection would do a lot in that regard."
Some Republicans are worried that image of a social warrior could turn off independent voters who will be critical to attract in November.
Others on the right have been critical of Pence, citing his handling of debate in Indiana over a religious liberty bill that conservatives fought to pass.
Erick Erickson, a conservative media figure, penned a scathing column in his "Resurgent" publication on Monday, saying about the fight and public posture on that issue that "during that fight there was real bitterness in the evangelical community that Pence clearly did not have the courage of his convictions." When national attention highlighted the controversy over the bill, Erickson added that "Pence folded like a cheap suit."
Hatch took issue with Erickson's criticism, saying, "Some of the critics don't take into consideration that as governor, you have to represent everybody. So it isn't easy just to be a dictator."
Wisconsin GOP Sen. Ron Johnson compared Trump picking Pence to 2012 GOP nominee Mitt Romney selecting Ryan, "who really had the Washington experience, the legislative experience. It's crucial. If you have to get something done and you don't have that experience, let's face it, this is an alternate universe here so you need someone who understands the place. I think he would be a good pick."