"How can you, with any compassion, cut so much money that you cut even the amount of money under the present budget, and you cut 9 percent below the level now mandated by across-the-board spending cuts, by sequestration?" Jackson Lee asked on the House floor.

"It was a bill destined to die, should have died, because it lacked compassion," she said, adding that the bill was "shameful."

Democrats have argued for weeks that Republicans are going too far in their pursuit of a balanced budget by cutting discretionary programs, without doing enough to cut military spending and raising taxes. Jackson Lee said the GOP's focus is undermining the needs of constituents.

"The federal government is an umbrella on a rainy day," she said. "It is the engine of the economy, it is the answer to issues, such as transportation and housing."

The split within the Republican Party seems to indicate that there are limits to which the GOP can continue to cut discretionary programs without losing GOP votes.

In the meantime, Congress faces two tests in the fall on the issue of spending. When Congress returns in September, it will face the task of agreeing to a continuing spending resolution for 2014, and then later on, a debt ceiling agreement will need to be reached.