MANCHESTER, N.H. — Senator Marco Rubio of Florida landed here at 2 a.m. on Tuesday, bleary but beaming from a surprisingly strong showing in Iowa, and confronted growing expectations from his party’s establishment that he may be the best equipped to unite Republicans.

Mr. Rubio’s tally in Iowa — where he received 23 percent of the vote and came within one point of Donald J. Trump — gave his campaign another jolt of energy at a time when good fortune seems to be breaking his way. Wall Street financiers are increasingly moving to support him, as disclosures this week by a “super PAC” backing him made clear. He picked up a coveted endorsement in South Carolina from Senator Tim Scott, the lone black Republican in the Senate.

His campaign appears to be leaving little to chance, aware that a lackluster result here would greatly diminish him. He began a week of morning-to-night campaigning early on Tuesday, stopping at a diner before dawn to work the room, field congratulations and issue a plea for support.

“We need your help,” he said. “We’ve got a lot of work to do here in New Hampshire.” As he walked from table to table, one well-wisher passed him a clear plastic bag with several cigars in it. Mr. Rubio, who is of Cuban descent, accepted them and smiled. “Maybe we’ll save them for Tuesday night,” he said.