Can I get fired for being out of work due to an illness requiring surgery?

IF you use sick days you still have, you cannot be terminated for using them: sick days which you earn are part of your compensation (or pay), and terminating you for using them would be to deny you part of the compensation you worked for, which is illegal. You could sue if fired for using sick days.
If you want to use vacation days but did not schedule their use in advance, your company could deny you their use if the timing is bad (busy time, short staffed, important project, etc.). While you have to be allowed to use vacation days the same as sick days, unlike sick days, the company has a say in "when" you use them and can deny you vacation when it's a bad time for the company. If you were denied use of the days when you wanted to use them but were out any way, you could be terminated.
If you simply miss work without properly using sick or vacation days (see above), you could be terminated unless you company is covered by the Family and Medical Leave Act (FMLA) (at least 50 employees within a 75-mile radius) and you are eligible for it (you've worked there long enough--more than 1 year--but would also have to have worked at least 1,250 hours in the last 12 months). Unless you use PTO (paid time off; sick or vacation days) properly or FMLA leave, there is no inherent right to miss work for medical reasons or surgery and you could be terminated.