I am currently attending a CC in hopes of transferring as a computer science major.
Since CS is a highly impacted major, I was wondering if it is possible to transfer to a UC (mostly UCLA) after having 2 W’s on my transcript? Should I just give up hope on attempting to transfer to UCLA?
W’s do not matter when transferring to a UC. Personally, ive acquired 4 or 5 W’s and received admission to UCLA for chem. Hope this helped! 
Yes not a big deal. But it depends what the W’s are in? Are they in your major prep like discrete structures or C++/Java programming courses? Might be a issue to raise concern, but if you bounce back and can get an A in the course, it should not be an issue.
Lastly, when you apply for the UC’s, on the UC application they have an extra comment section where you can explain why you have the W’s (i.e. family issues, or health reasons, etc.).