Can my boss threaten to fire me if I don’t vote for Romney?

No.

You’ve seen reports recently where employers have sent emails to their employees attempting to convince them to vote a certain way. Of course, the 1st amendment protects an employer’s speech and an employer may state his or her opinion. Here is a link to one such article:

https://news.cincinnati.com/article/20121101/NEWS/311010033/Memo-from-boss-Vote-Romney

There is a federal law which prohibits such conduct.

It provides:

No person, whether acting under color of law or otherwise, shall intimidate, threaten, coerce, or attempt to intimidate, threaten, or coerce any other person for the purpose of interfering with the right of such other person to vote or to vote as he may choose, or of causing such other person to vote for, or not to vote for, any candidate for the office of President, Vice President, presidential elector, Member of the Senate, or Member of the House of Representatives, Delegates or Commissioners from the Territories or possessions, at any general, special, or primary election held solely or in part for the purpose of selecting or electing any such candidate. 42 U.S.C.A. § 1971.

So, if your employer threatens to fire you if you vote for Obama, tell them about this law.