Texas GOP lawmakers are calling the Obamacare vote a victory.
Senator Ted Cruz remains one of the most vocal supporters of the "De-fund Obamacare" push.
Following Friday's vote, Cruz issued a statement encouraging GOP senators to filibuster the resolution.
Republicans stand united in their opposition to the health care law.
We spoke with U.S. Representatives Bill Flores of Bryan and John Carter of Round Rock by phone Friday.
Both said a majority of their constituents are in support of the house's resolution.
"For every 100 calls we get, 95 of them say don't shutdown the government but do stop Obamacare," said Flores.
"In our district, it's not any different," said Carter. "They want something done with Obamacare because it's quite honestly costing too much and not going to be successful."
In a statement issued following Friday's House vote, Texas Senator John Cornyn's office said, "Sen. Cornyn has voted to defund Obamacare every time it has come up for a vote and will continue to work to protect Texans. We hope, when deciding how to proceed with the CR, Majority Leader Reid will listen to the overwhelming majority of Americans who do not want Obamacare."
The House reconvenes Wednesday.
Representatives will then begin addressing the debt ceiling.
Flores said provisions to stop, or at least delay Obamacare, will also be included in the debt ceiling.