Can electrical engineers do computer science jobs? How much different is CS and EE when it comes to CS knowledge?

As a current CS student, it's hard to accept that I may have wasted time taking CS courses if the future of this industry is uncertain when it comes to job stability. I was thinking of switching my major to EE, since I've heard that it's a major that can do CS jobs but CS majors cannot do EE jobs. Ideally I want to do SWE jobs but the new grads are struggling in this market, and I don't want to end up in a situation where I'm 1-2 years unemployed out of graduation without internships (if I don't end up landing one) and then I'm practically done for in the eyes of recruiters. I wonder if the EE entry level job market is much better so I may eventually switch to SWE someday.