Why don't members of House of Representatives use their power?

When Democrats control the House of Representatives, left leaning "progressives" are the majority, and their agenda is way more liberal than the Senate and the President (or Presidential candidate).  Likewise now, as Republicans control the House they are more "conservative" than others in power.
Why don't they use their power when it really matters to advance their agenda as much as they can?  Democrats could have refused to fund the Iraq War.  Republicans could have refused to fund the Affordable Care Act.  Democrats could have let Bush tax cuts expire.  Republicans could have let unemployment insurance lapse years ago.

The answer is that during their campaigns these "extreme" partisans lie to the American people about what they can and will do when they get to Washington.  It's no mistake that the less the chance of winning either their election or a majority in the Congress, the more extreme the promised change becomes.

Every so often (lately 2006, and 2010) America has wave elections where basically all of the close elections go for the same party.  This means that people who began with little chance, and consequently making bold promises, wind up winning.  Ironically, at the time they meant what they said except for the belief that it could actually happen.

Once the true reality of our Democracy is at hand, sober minded members of both parties get enough of the partisans to go "native" and compromise is in the air.

So ultimately public opinion wins.  Because the leaders of the House aspire to stay there.  Also because they become statesmen actually trying to do what's right for the country.

That's why many members of the House don't use their power as they promised.
And it's a good thing.