In the US it is possible in most states to terminate an employee for no reason, so yes, you can be fired if he disagrees with anything you say that he becomes aware of. However, the likelihood of it happens is generally in direct correlation to how he sees what you said as a threat to the reputation of the company or to the profitability of the company. Let's take some examples.
If the business is one where they provide services (such as database support) to candidates for office for a particular provider, then expressing that you are strong Republican while working for a company whose customers are Democratic party elected officials, candidates and managers is definitely likely to get you fired. You might have access to data that the opposite party could use or you might be tempted to in some way sabotage their data.
If you expressed political views that might be considered hateful to one group of people and those people are potential customers, then you could likely get fired. This could have the effect of making customers unhappy, and if it is between firing someone and making customers unhappy, well customers are usually going to have the edge in that equation.
Most reasonable people would not fire you for supporting a candidate of the "wrong" party. However, there are some CEOS who are strongly in favor of one party or another and have made a public issue of being on that side (think Hobby Lobby which is strongly Republican). Those CEOs could well think that supporting the other party shows a severe lack of judgement. There have been cases where people were fired for having bumper stickers of the wrong party on their car. If you know your CEO is one of these types of people, then keep your mouth shut if you disagree and want to keep your job. Generally you know when you work for one of these companies because they want to tell you who to vote for or they want you to contribute to the party of their choice as a condition for employment. (Personally I would not consider working for such a company unless I was going to starve otherwise even if I agreed with the party they espouse because it is dangerous to the public good to try to suppress the other party as illegitimate.)
It also can depend on how public the public expression of your views is. Getting arrested in a public protest and being on the news is more likely to get your fired than chatting to a friend where a manager can over hear. Companies have the right to manage their public image, so the more public and the more controversial what you say is, the more likely you are to get in trouble for it. This is especially true if you are wearing a shirt with the company logo or are otherwise widely known to be an employee of that company or are at a public event (such as a conference) in a role of directly representing the company.
Now none of this infringes your right to free speech in any way. The constitution guarantees the government will not arrest you for what you say, not that your speech is without consequences ever. All speech has potential consequences. Telling your wife she looks fat has possible consequences as well as telling your boss he is an idiot. Expressing unpopular political views can make people stop being your friend or not want to hire you or indeed they can fire you. People are going to judge you on what you say and if they find it means they think less of you then indeed it can have consequences for your career. I am not saying you should not express political opinions out of fear, but that you should consider the context and the likelihood of it affecting your career before speaking. If being a strong Republican who supports tossing all Muslims out of the country is important to you, then you might look for a job where you are working with like-minded people and you can speechify all you want. Same if you think that abortion should be safe and legal to take an issue from the other side.
If you are worried about how your manager will react, then think before you speak. You can express more controversial views in a more private space.