It's all rhetoric. These guys are all about making the other look bad...
When it came to the budget issue, Republicans say Obama needs to be a better leader and take control. He needs to propose a bill; Obama is the president, he needs to start "acting like one."
When it comes to immigration, Rubio (read Republicans) says Obama needs to leave it alone and let them work it out. "How can Obama draft a bill without talking to Republicans?" I mean in all seriousness, with as much media coverage, you'd think Obama's staff knows where Republicans stand on the immigration issue.