House Republicans desperately want their party to pick up seats in the midterm elections -- Senate seats.

Frustrated by President Obama's unwillingness to negotiate and fed up with Senate Majority Leader Harry Reid for burying hundreds of bills they have passed since winning control of the House in 2010, they are approaching the 2014 elections differently than usual. They want to do what they can to help -- and in particular, not hurt -- their party's chances of taking back the Senate, instead of focusing exclusively on their own re-elections.

“We could have a much different next two years, '15 and '16, if there's a Republican Senate,” said Rep. Tom Cole, R-Okla., who is aligned with House GOP leadership. “It's not even just our majority we have to protect -- we have to protect the prospects of getting that Senate win. It matters.”

The desire to see their party flip the Senate has been playing a role in House Republicans' decision-making since October's government shutdown. The episode was so bad for the GOP it threatened their House majority. Compromises with Senate Democrats on the budget and farm bills and a virtual surrender on the debt ceiling were partly driven by a desire to avoid another politically dangerous impasse.

Between now and Election Day, expect House Republicans to broadly consider how their legislation and political messaging might affect Senate Republicans. Excited by the possibility of what a united GOP Congress could accomplish, they're shelving their traditional rivalry with the Senate -- the late Democratic House Speaker Tip O'Neill once reportedly said that House Republicans are "the opposition. The Senate is the enemy."

The November elections have led them to pitch comprehensive tax reform and float the idea of proposing an alternative to Obamacare. Neither has the potential to become law in the current Congress, but many House Republicans believe the election prospects for them and their Senate brethren depend on offering the voters a positive agenda that would set the stage for negotiations with Obama in 2015.

“The president will still veto a lot of the stuff that we pass, and we won't have veto-proof majorities. But at least we'll be able to contrast to the American people what we would do,” said Idaho Rep. Raul Labrador, a Republican who is aligned with the Tea Party. “Right now Harry Reid's willing to just lay on the grenade. He takes all the shrapnel.”

Republicans need to gain six seats on Nov. 5 to flip the Senate, and their hopes could rely on five House Republicans who are running for spots in the upper chamber: Rep. Bill Cassidy is challenging Sen. Mary Landrieu, D-La.; Rep. Tom Cotton is challenging Sen. Mark Pryor, D-Ark.; Rep. Steve Daines is challenging appointed Sen. John Walsh, D-Mont.; Rep. Shelley Moore Capito is running for an open seat in West Virginia; and Rep. Cory Gardner is challenging Sen. Mark Udall, D-Colo.

The Republicans' path to victory runs directly through red states where Obama and his signature health care law are unpopular. The GOP must survive a tumultuous primary season that could result in the nomination of another batch of weak general election candidates, but at this early stage their prospects are bright. The Republicans' House majority now appears secure -- the result of Obama's political troubles and redistricting that strengthened the partisanship of House seats.

To be sure, not all House Republicans agree that the Senate elections should influence their election-year strategy. And increasing their own majority remains their top priority. Still, a majority of House Republicans are focused at least somewhat on their party winning the Senate.

“If there’s one thing I’d like to do, it’s make Harry Reid a minority leader,” said Rep. Jason Chaffetz, R-Utah. “Winning back the Senate is critical.”