Analysis by Z. Byron Wolf, CNN

(CNN) -- One of the first things Donald Trump did as President was to file official paperwork that he'd qualify as a candidate in 2020.

He's hired a campaign manager. He's already got a re-election ad.

He talks a lot about how he'll be in office for eight years.

"We'll be here another seven years, hopefully," he said, for instance, at one recent White House meeting.

His press secretary has dismissed the idea that he would ever not run in November of 2020.

"Of course he's running for re-election," Sarah Sanders told reporters last summer.

This is happening, people.

But that has not stopped at least one Republican senator from saying he doesn't know if Trump will run and his ex-wife from publicly saying she doesn't think he should be on the ballot for Republicans in 924 days.

"He has a good life and he has everything," Trump's first wife Ivana Trump told Page Six in an interview published Monday. "Donald is going to be 74, 73 for the next (election) and maybe he should just go and play golf and enjoy his fortune. ... I'll tell you something, I don't think it's necessary."

That may be the Trump she knows, but fading off into retirement does not sound much like the one most Americans see on TV.

Her comments come a few days after Republican Sen. Bob Corker of Tennessee, who has tangled with Trump on some issues, said he was not yet convinced the President would run.

"I have no idea whether the President will run for re-election, nor what the field will be on the Republican side, so I think it's way too early to weigh in on who won my support," Corker told CNN's "New Day" co-anchor Alisyn Camerota.

"But are you saying you're not sure the President is going to run?" Camerota asked.

"I'm definitely not sure if he's going to run," Corker said.

Other Republicans haven't questioned whether he'll run, but they have not endorsed him.

"It's way too early to be talking about 2020," Wisconsin's Republican Sen. Ron Johnson told CNN's Chris Cuomo on Thursday. "It could be a completely different world by 2020. We have a 2018 election first."

Indeed it could. Republicans could very well lose control of one or both chambers in Congress this November, and that could lead to a very different profile for the President, who has had trouble playing nicely with Congress when his party controls it. Having Democrats to spar with would change things quite a bit.

CNN's Manu Raju found a surprising number of Republicans, like Johnson, who are unwilling yet to endorse Trump's re-election, which is a much different thing from thinking he won't run, but it's just as fascinating that Republicans want distance from the man who has changed their party so much.

There are also a few Republicans, like Ohio Gov. John Kasich and Sen. Jeff Flake of Arizona, who have toyed with the idea of a primary challenge against Trump.

Such challenges of a sitting President don't ever work, but they can do mortal damage to a presidency: Ted Kennedy challenging Jimmy Carter and Pat Buchanan challenging George H.W. Bush are two examples.

There is also the sense it could make for someone like Trump, who is historically unpopular at this point in this term, to get out before he loses.

More than half of Americans do not think he will be re-elected, by the way, but it's such a premature question as to not be meaningful. And it puts him in good company: A lot of ultimately re-elected presidents caused similar skepticism among voters.

On the one hand, leaving office might make a little bit of sense for him. He'd have a perfect electoral record and he could say he was done with the work of changing Washington. You don't have to psychoanalyze Trump to say that he does not like failure and he does not like losing. It's far from clear what kind of candidate Democrats will pick, but no matter who it is, the possibility of defeat is very real for the President.

But it's equally hard to see someone like Trump simply stepping down without some kind of excuse. He seems to like being in charge too much, and giving up would be totally out of character, as has been written by CNN's Chris Cillizza in the past.

From Trump's repeated references to serving two terms and the official steps he's taken to move in that direction, it's hard to believe otherwise.

But the speculation of his former wife is not going to make the theory that Trump won't run for re-election go away, no matter what the evidence is.