Trumps EO regarding elections and citizenship may or may not change our elections much.

You cannot generally tell states how to handle elections as far as the law goes, but withholding funds might be a whole other ballgame.

I am sure the lawsuits will come fast and furious over this one. I am pretty sure that the Government will even lose the bulk of the legal arguments. But the one thing that Trump may have up his sleeve is the threat to withhold federal funding.

Unless said federal funding is guaranteed at some point by someone, it is generally considered optional and up to the discretion of the executive. There have been plenty of lawsuits over the years demanding that states (and universities, etc...) are entitled to federal funding without conditions, but these generally come back on the side of the Administration. Look at how Maine ended up caving over the trans-athlete issue over the past few weeks. Even with as much help the left is getting from certain District Court Judges, the University and State of Maine did not want to go there.

The idea of having to prove your citizenship to legally vote is a popular idea and quite intuitive as well. We legally do not allow non-citizens to vote, so why is there resistance to this? The answer, of course, is obvious. Some people feel like they need to cheat to win and any thing that takes away their ability to do so, is a bad thing. You know, possibly racist and bigoted as well. They will fight to the death to keep that non-citizen advantage going.