Mr. Rubio wasn’t supposed to be here at all. A rising superstar in his party with a personality and background that thrilled donors, Mr. Rubio was in the top tier of Republican presidential hopefuls in 2016. Many in Washington believed he would be the nominee, a candidate who would finally broaden the party’s appeal with Hispanics while holding true conservative credentials.

Openly antagonistic about the slow pace of the hidebound Senate, Mr. Rubio made it clear that it was the White House or bust. And bust it was as Donald J. Trump upended him in the Florida primary race. But after insisting he would give up his seat at the end of his term, Mr. Rubio instead decided to run, citing second thoughts about public service that were prompted by the mass shooting at the Pulse nightclub in Orlando, Fla.

It was not without risk. “Losing two elections in a year has never been part of my plan for life,” Mr. Rubio said.

He won and re-entered an institution that allies said he found frustrating. Mr. Rubio wouldn’t be the first senator to rate his experience as a second-term lawmaker an improvement over the first. Figuring out the Senate can take time, and more-senior lawmakers might not even begin to take colleagues seriously until they have at least one term under their belts.

“I’m at 58 in seniority,” Mr. Rubio noted. “I came in at 99.”

Mr. Rubio, who has close friends in Puerto Rico and visited soon after Hurricane Maria had passed, said that he had no quarrel with the federal response, but that the conventional reaction to a severe hurricane didn’t suffice for the already struggling island.

“The problem,” he said, “is that the model that works in Florida and in Texas doesn’t work as well in Puerto Rico for a lot of reasons: the geographic isolation, the pre-existing challenges and the fact that they had just previously been impacted by a storm.”

As for his relationship with Mr. Trump — who ridiculed Mr. Rubio as “Little Marco” during primary race debates, prompting Mr. Rubio to try to get under his opponent’s skin by noting his “small hands” — Mr. Rubio said those jabs did not extend beyond the campaign stage.