It is possible that you could get fired if you do not go to work on Sunday due to religious purposes. This is because in case you needed not to be attending work on this day, you should have mentioned it to your employer before signing the contract. It would be best that you talk to your employer first or check your state's labor laws for clarification on this.
I agree with Hyachintha. I'd like to add that if this religious belief is new and therefore you couldn't have mentioned it BEFORE you were hired, then you should tell your employer immediately. There is no guarantee that they can accommodate your beliefs, but you need to discuss it. Good luck! :)
If the agreement was that you be available on weekends, then you can be terminated. Usually they will accomodate you by cutting your hours (not just on sunday) to allow you to go to church, because they have to hire someone else to cover your agreed on shift.
You are going to have to work something out with your employer. Routinely refusing to come in for a scheduled shift is going to lead to problems one way or another. If you're not having to do it all the time, you might find someone who's willing to trade your Sunday shift for one of their shifts on another day.
Some businesses like retail and restaurants are busy all days, and they try to accommodate their workers but will give preference to their employees that are flexible on work dates. If its important to you, I advise finding a career that doesn't challenge your moral restrictions.
Every religion has their days in which work is not advised. You can worship in other ways besides being present at gatherings. In America, yes, you can get fired for not working on Sunday if your work requires you to be there. It's not the same as in the rest of the world where many times these things are automatically understood.
If you made that clear to the plotter before being hired and they cleared it you'll be fine. If however, you didn't mention having to be off on Sunday before being hired, you will likely have a problem.
As various people have said, it would have been ideal if this had been brought up prior to accepting employment; but you also have the right to "convert" to a religion that requires such observances.
There are federal laws that require "reasonable accommodation" for such beliefs but I think they do not apply to all sized companies. (And not all accommodations requested would qualify as "reasonable.")
You will need to do some research online and / or talk to a lawyer.