party roles

Just because you don't have control of a legislative body doesn't mean that your party can't still control the way the chamber works.

America's founding father's were so obsessively paranoid that a small minority would come to popularity, get themselves elected, seize power and hold on tight that the US federal system especially is intentionally hamstrung.
Consider that one a second, they pretty much intentionally made it hard to get anything done.

Of course that leads to an entirely different problem, a small minority can get a few congressmen elected, and gum up the whole works. Now sure the senate especially has changed that, with new cloture rules, but things haven't changed that drastically.

The minority may not have the power to cause events, but they certainly, especially in a binary system like the US, especially with numbers in congress always having a fair balance of Democrats and Republicans, have the ability to gum up the works.

Now in this process of staunchly preventing government from doing anything at all, they can use this threat to extract heavy concessions from the majority party, under threat of avoiding any action at all.
In this way permanent parity is established: though one party may have the majority, so long as they are sufficiently disunited or not in enough control, you can still ensure that your platform is not utterly ignored.