"There's a possibility that he won't get 50 percent on the first ballot," Bush told CNN's Jamie Gangel on Friday. "And if he doesn't do that, there are a whole lot of people who don't believe he's the proper guy."
Asked whether he thinks the Republican party should rally around Trump if he does become the nominee, Bush, who has publicly endorsed Texas Sen. Ted Cruz, simply replied, "I think they should support Ted Cruz."
The former Florida governor added that Cruz's decision to tap former GOP hopeful Carly Fiorina as his vice president was a "smart move."
"She takes on Trump really well, I think, and she takes on Hillary Clinton very well as well," Bush said. "Someone who's got a proven record and who's been vetted as a candidate, I thought, was a smart move by Ted Cruz."
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Pointing to Trump's speech Wednesday on foreign policy, Bush said he thinks the billionaire businessman is "not a serious person."
"I don't know which Donald Trump to believe, the one that read from a teleprompter a speech that was inside the lines or the one that wants to build a wall and make Mexico pay for it, which Donald Trump is the one that's expressing these views," Bush said. "There's two of them and I think we need a president with a steady hand."
If Trump is the GOP nominee, Bush added, "we'll lose the Senate and we'll lose the presidency in a landslide."
Some of Bush's fellow Republicans seem less certain of the party's chances of blocking Trump from the nomination.
Former Speaker Newt Gingrich told The Washington Post, "Trump has become a fact rather than a problem. Show me mathematically how you're going to stop him. This all assumes, by the way, that the guy who wrote The Art of the Deal can't figure out a way to make a deal with the undecided delegates."
And RNC member Ron Kaufman, who is close to Mitt Romney and George H.W. Bush, said, "More and more Republicans are believing that Trump is the inevitable nominee. They're accepting the fact that he's the nominee and looking forward to moving on."