Electrical engineers in my school with an embedded systems concentration (near equivalent of CpE at most other schools, with more extensive electrical background) haven't had much trouble finding jobs. However, most of the jobs tend to be in Oregon (Hillsboro, Beaverton), California (Bay Area, San Diego), and Texas (Austin). If you're passion is in doing CpE and hardware design, you will most likely need to relocate, whereas Comp Sci majors can find a job pretty much anywhere.
Networking is key in landing interviews and job opportunities, in my opinion. Also make sure your resume is rock solid and is creative enough to pop out among the 1000+ resumes that recruiters look through every day.