Not in Texas, sort of. In other states, workers may have no such protection, at all. See the website, Can My Boss Do That? here.
Mitt Romney has been quoted as encouraging employers to tell their employees how to vote. See Mike Elk’s blog post. In this time of secret ballots, it would be hard for any employer to enforce such guidance. The U.S. Constitution via the First Amendment would not protect most employees from coercion, assuming the employee does not speaking out to others about how s/he would vote.
According to Mike Elk, the Citizens United decision a couple of years ago overturned Federal Election Commission rules which formerly prevented employers from political campaigning among their employees. In a phone call with small business owners, Gov. Romney assured the business owners that there is nothing illegal about campaigning among their employees. He may be right in most states. But in Texas, the Texas Election Code, Art. 276.001 prohibits anyone from directing another person how to vote and from asking how the person voted. The statute specifically prohibits one who has "authority in the scope of employment" from telling another how to vote. That means employers.
Of course, the Texas statute is a criminal offense, not a civil offense. It is not likely that a busy District Attorney’s office would take the time to deal with a relatively minor crime like like voter intimidation. So, if the D.A. does nothing, the average worker is out of options. But, shoot, we’ll take whatever we can get…..