As for the issues that you mentioned: I think it's important that Republicans recognize how much leverage they actually have. Repealing health care reform and/or extending all of the Bush tax cuts is flat-out not going to happen. Obama doesn't NEED to compromise at all; he already got his way, and if Congress takes no action, the status quo is the Democratic position. At most, the Republicans might be able to work with the Democrats to change the laws in ways that are mutually agreeable to all of them.
As for the other two issues you mentioned. Cap-and-trade was already dead on arrival, so I doubt it's on the agenda at all. For that matter, neither is immigration reform...at least not as a serious policy change (although the Dems might introduce it as a wedge issue knowing that it will lose).