Sen. Jeff Flake, R-Ariz., won rave reviews in the press last week by delaying President Trump's Supreme Court nominee, and followed that up with a Monday visit to New Hampshire, stoking speculation that he could be setting up a run against Trump.

But many in his own party say they doubt he'll get far.

"Maybe it's trying to see if there's life after [the Senate], but I don't understand it," said one Republican senator who asked to remain unidentified. "Anytime people go to those places, it makes you wonder ... I just don't see it."

Another GOP senator wondered why and how Flake could take the plunge if he wasn't even willing to do so for re-election in Arizona — Flake dropped out after most polls said he didn't have a chance. That's raising real doubts among Republicans about how Flake could mount a national challenge to Trump, who is enjoying rock-solid popularity among Republican voters after nearly two years in office.

Flake won praise mostly from Democrats after he warned his GOP colleagues that he wouldn't support Supreme Court nominee Brett Kavanaugh until a more thorough FBI investigation was completed on the nominee's alleged sexual assaults against women. Flake said he wanted a pause because the country was being "ripped apart" by the fight over Kavanaugh.

Just days later, Flake arrived in New Hampshire to deliver a 25-minute address at Saint Anselm College to criticize the polarization of politics that touched on his game-changing move last week.

Flake has positioned himself as one of few GOP voices who regularly criticizes Trump's bombastic and sometimes mean approach to fighting his political enemies, which led Trump to call for his removal. Some say Flake could be the one to move the GOP away from Trump, and in New Hampshire, there appears to be some appetite for a primary challenge to the president.

According to a New Hampshire Journal poll taken in late August, 40 percent of New Hampshire Republicans believe a challenge to Trump "would be a good thing." Another poll taken in late September by the American Research Group showed that 33 percent of New Hampshire Republicans disapprove of Trump's job, compared to 64 percent who approve.

"There are at least a significant number of Republicans ... who are eager to send a message," said Fergus Cullen, a former New Hampshire GOP chairman and an anti-Trump voice. "We are disgusted by this administration — and we are just waiting for a vehicle to emerge ... Maybe the vehicle is Flake, maybe it’s [Ohio Gov. John] Kasich, maybe it’s not someone on the radar today."

In the speech Monday, Flake spoke openly about his standing in the party, noting that at times he feels he is a senator without one. He also all but ruled out an independent bid for the presidency, maintaining that he is and always has been a Republican, even though he admitted he's somewhat on the outs among GOP voters.

"I've been failing my tribe for some time now," Flake said in the speech. "Well, by the ways we measure political success in this sordid era, and by the conventions of how party loyalists are supposed to behave, I hope to continue to fail my tribe."

"Independent, that's a tough road," Flake told reporters after. "I'm a lifelong Republican. This is my party. It's been tough to see the direction of it ... I'm not sure there's a home in another party."

The trip was Flake's second of the year to the first-in-the-nation primary state, having made the trip up in March for "politics and eggs," hosted also by St. Anselm College. While a primary contest is way off, GOP members weren't completely surprised he made the trip.

"Not really," said Sen. Bob Corker, R-Tenn., the other Senate Republican retiring from his seat at the end of the year.

One Arizona GOP strategist believes there is a 20 percent chance Flake takes the ultimate plunge next year, but real questions remain concerning his family and whether he wants to put them through a grueling primary against a sitting president.

"I think the appetite is there," the strategist said. "The real question I have is does he want to do it? From a policy standpoint and for how the president treats others, that's a real problem for him, obviously. But does he want to put himself and his family through this for 1 1/2-2 years? I just don't think he has an answer yet, which is why he's going to continue to do these kinds of things."

Flake is expected to return to Washington this week as the Senate opens consideration to Kavanaugh on the floor, which is expected to last until the FBI investigation wraps up. However, he is not ruling out future trips to the Granite State.

"We'll see," he told reporters when asked if he might return.