I don't see how he is going to be able to do this unless there is a statute that allows to set the rules for federal elections. You can't argue state's rights for abortion and then turn around and do this.
Yes and no.. I believe that he can at the federal level which would leave places with the weird and obviously embarrassing need to run elections with two sets of rules.
The disparity would, hopefully, speak for itself.
And there are tons of ways to bully a state into line. Take Montanas back of speed limits for years and years, until the feds just stopped sending highway money to us. Montana pissed and moaned but eventually our highways were crumbling and we fell in step.