Such an act is known as Bipartisanship. It will depend on the bill in question. There are some thing that Democrats will compromise on, and some things they won't. There are also things Republicans can do to get Democrats to agree with their legislation. Here is where I disconnect with you, correct me if I'm wrong, but you seem to have the idea that Liberals are no longer going to be an obstacle to you. Make no mistake, the Democrats still have more power than the Republicans do, just not as much more power. The President is still Obama, and the Democrats will still attempt to forward their agenda.