I believe anyone who has been a Senator for a short time will and should have problems. Our next President needs to be someone with some actual governing experience. I hope I don't have to vote for a Senator to be our next President and I won't even vote if a Representative from the House is the GOP nominee.
I doubt it'll matter. It demonstrates that he's either an imbecile or a liar, but his whole election campaign will be built around capturing the votes of the plurality of Americans who are imbeciles, so it's unlikely to hurt him. In the primary, that kind of flat-eartherism will actually be an advantage, and in the general election, anyone who cares enough about science or the environment for it to be a decisive factor in their voting choice was almost certainly not going to vote Republican, anyway, even if the nominee hadn't been a climate denialist.