Hi Alexa,
The specific likelihood that you will be able to find funding as a Master's student will vary fairly widely from program-to-program. I do think it is realistic that you will be able to find at least partial funding if you are attending a R1 university with an active research program. That doesn't mean it will be easy — you will have lots of competition. But the opportunities are there. Here are two:
1) Research assistantships: You are right that most funding is earmarked for Ph.D. students: partially, this is because Ph.D. tuitions and stipends are guaranteed* and so until a faculty member has enough funds to support their Ph.D. students, that will be the priority. However, sometimes faculty have small amounts of money for short-term projects that none of their Ph.D. students are actively working on, or for which they haven't been able to recruit a Ph.D. student. I would seek out faculty with new grants, in particular. Look at their websites and see if they have a grant that was funded in the last year — there's a good chance they need more people working on that project as it is starting up. I've hired several MS students as research assistants this way.
2) Teaching assistantships: Most CS departments have skyrocketing enrollments and a voracious appetite for TAs. Your best bet is to seek out classes with particularly large enrollments — e.g., required courses for all CS majors. Many departments have student:TA ratios between 25:1 (e.g., at Georgia Tech, where I previously worked) to 60:1 (at U Michigan, last I checked). So, at Georgia Tech, a class with 300 enrolled students would have room for as many as 12 TAs. When you seek out the smaller enrollment classes, there's a good chance the instructor already has a TA in mind. But, with these large enrollment classes, many faculty need to reach outside of the students they directly know.
* At any competitive R1, at least.
Hope that helps.