During Clinton's second term, when both houses were held by the GOP, a great deal was able to be accomplished by bi-partisan legislation. The Republicans now need to be able to demonstrate they can be pragmatic and capable of governing going into the 2016 presidential elections. On the other hand, President Obama will be concerned about his legacy. Therefore, significant progress may be able to be made, with compromise, on immigration reform, the federal budget, energy policy and modifications of both the Affordable Care Act and Dodd Frank financial regulations.
Senator Mitch McConnell has indicated that he didn't expect to be able to repeal the healthcare law, stating "It would take sixty votes in the Senate" and "nobody thinks we are going to have 60 votes". Obama will still maintain significant control with the presidential veto. On the other hand, he will have little incentive for any compromises with a Democratic Senate that continues to be lead by Harry Reid.
Jonah Goldberg (L.A. Times) - A D.C. cure: Take the hard votes
"That said, in the spirit of compromise so lacking in Washington, I would like to offer a suggestion for how to fix the alleged problems of partisanship and gridlock: more partisanship about ideas and less about process."
Western Journalism - Harry Reid Just Got His Legs Cut Out From Underneath Him…By A Fellow Dem
"South Dakota Democratic Senate candidate Rick Weiland started a national petition Friday for Reid to be removed as Senate Majority Leader, replacing him with either Massachusetts Senator Elizabeth Warren, Illinois Senator Dick Durbin, or Independent Senator Bernie Sanders of Vermont, according to The Hill."
Harry Reid's Plot to Keep the Senate (Far Center Blog Post on that Politico article)