The GOP controlled House (meaning leadership) would rather file a lawsuit (pay lawyers to do their dirty work) than exercise the most powerful tool available. The power of the purse.
Boehner said it best, [paraphrased] once inside the beltway, he realized he couldn't fight them, so he joined them.
It has been demonstrated over and over and over that the House lacks the raw political power to control the purse.
The Senate will not allow House control over money