I'd guess there's a pretty good argument that such a law in the US would be unconstitutional -- unless, perhaps, the voting options included the right to cast a ballot that said, in effect, "I choose not to vote." Freedom of speech generally includes freedom of association, and freedom of association generally includes freedom of non-association -- that is, I have the right not to associate with (i.e., not to be linked to in such a way as to appear to agree with or endorse) any person or group I don't want to associate with. If you make me vote for a candidate -- or even if you make me vote for anyone (via a write-in ballot) -- you are arguably forcing me to associate with that person.

Having just written the above, I then surfed around a bit. There does indeed seem to be a suggestion that mandatory voting would be unconstitutional unless an "NCA [No Candidate Acceptable] option" were included. Here's an article by John Dean (of all people).

• John Dean on Mandatory Voting Laws