There are a lot of stupid things in this movie.

But maybe the stupidest was just to schedule a presidential election like you would in a parliamentary system such as England. Lindberg disappears, his wife says, "Please just hold an election in November" (two years before it is scheduled).
There is this little thing called the constitution. To do what was shown here would require a constitutional amendment ratified by 3/4 of the states. That could not be done within a few months. I don't know if this came from Roth's book, but, if so, he was a dimwit. Course, this whole story is very simple-minded, with no nuance.