A few hours before President Obama was scheduled to deliver the State of the Union address on Tuesday, Senator Mitch McConnell, the minority leader, mentioned to Senate Republicans in their closed-door luncheon that Marco Rubio would be delivering the party’s response.

Rubio jumped up and said, “I am?” His colleagues laughed.

That’s how Senator Ron Johnson of Wisconsin tells it. Rubio, whose rapid rise has been exhaustively chronicled, has made quite an impression on his colleagues. In his two years in Congress, he’s gained the respect of members from both sides of the aisle and become a leading member of his caucus. And despite his feigned surprise, he is now one of the GOP’s chief spokesmen, the man who was tapped to deliver the most high-profile rebuttal of the year.

On Capitol Hill, though, what really stands out is how much his colleagues simply like having him around. Beyond the magazine covers and primetime speeches, he’s become a favorite within the institution.

“He’s got a wicked sense of humor,” says Senator Lindsey Graham (R., S.C.). “When we were flying overseas, he picked the movie Machete. You go watch it, and that tells a lot about his sense of humor.” (Rotten Tomatoes, a movie-review website, says that Machete is “messy, violent, shallow, and tasteless — and that’s precisely the point of one of the summer’s most cartoonishly enjoyable films.”)

The members of the Republican conference aren’t the only ones who notice his star power — over the last few weeks, the 42-year-old senator has made a plethora of media appearances in support of his immigration-reform proposals, and Time magazine declared him the “savior” of the GOP. The senator, an avid Tweeter, tweeted a quick response: “There is only one savior, and it is not me. #Jesus.”

But Rubio’s modest Tweet hasn’t lowered expectations. Senator Jeff Flake (R., Ariz.) says the flurry of coverage hasn’t been ignored. “It’s been interesting in the last week to be in the House gym with him when every television has him, and the Time magazine thing pops up,” he says. “But he takes it all in stride.”

Is all of the media attention a good workout incentive?

“Maybe that’s it!” says Flake with a laugh. “He tends to speed up a little!”

For now, though, Rubio and his staff don’t seem to be getting ahead of themselves.

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“You can’t be the guy that took down Charlie Crist in a political fight without also being keenly aware of how fleeting these moments in politics are,” says Todd Harris, a longtime Rubio strategist. “Charlie Crist was measuring drapes in the White House one day and persona non grata the next.”

Rubio’s latest endeavors have certainly courted disagreement. By bringing his conservative bona fides to a bipartisan group of senators pushing for comprehensive immigration reform, he’s made far-reaching reform possible. Not everyone is on board, of course — critics from the right call the proposal a thinly veiled push for amnesty, and many say that it could substantially increase entitlement expenditures.

But Rubio has run an aggressive PR campaign — with appearances on Mark Levin’s and Rush Limbaugh’s radio shows, no less — that has won grudging respect for the initiative from conservatives. Johnson, a fellow Tea Party darling, says he gives the senator “all kinds of credit” for making such a politically risky move.

Rubio’s efforts have been noticed by Democrats. Senator Chris Coons, a Delaware Democrat, says that despite his initial misgivings about working with someone from the opposite end of the ideological spectrum, the Florida Republican has won his respect.

Coons and Rubio ran into each other at the orientation for new senators and were “sort of polite,” Coons recalls, but they didn’t really talk until January. At his friend’s prompting, Coons bought a copy of Rubio’s book, American Son, and looked through it. He realized that many of the senator’s ideas “were just common-sense ways to make a government run more efficiently.” Soon after, he approached Rubio on the floor and said, “Look, I got your book, and I’m actually struck by how we might be able to agree on things.” They got to know each other, and have co-sponsored four bills since then, including the AGREE Act to promote entrepreneurship.

“He’s not just agile or slick,” Coons says. “He actually is a thoughtful person who tries to make sense of how we can get things done, even though he is a sharply ideological conservative.”

A GOP aide agrees that Rubio is good at bridging divides: “He’s sort of the emerging figurehead for the party in a lot of ways. He’s somebody who can unite the clans, and as much as a lot of us don’t like to think about differences on our side, it’s important to have somebody who can move past the infighting that Republicans have to deal with on a regular basis.”