House Republican leaders postponed a vote on government funding legislation until next week after many conservatives made it clear they wouldn't back it because it doesn't fully defund Obamacare.
The government will shut down if Congress does not approve a new annual spending plan by October 1, the start of the new federal budget year.
A vote on the bill, called a continuing resolution, to fund federal programs through December 15 had been slated for Thursday. No new date was announced.
But GOP leaders still struggled for support because many of their own members believe the language in the package on health care funding simply amounts to a "gimmick."
Since many House Republicans pledged to oppose any spending bill that doesn't also block money for Obamacare, Republican leaders crafted a plan to pair a spending blueprint with a separate resolution barring the use of federal funds to implement new health care law.
It also would require the Senate to vote on defunding the controversial health care law before it could vote on the short-term spending bill.
But conservatives object to that strategy because the Democratic-led Senate would likely reject the resolution and simply pass the spending bill that includes money for new healthcare programs.
The politically charged health care law was approved in 2010 and upheld by the Supreme Court last year. But conservatives are now taking aim at bureaucratic and funding steps required to get the programs running this fall.
Kansas Rep. Tim Huelskamp, slammed the House GOP proposal, calling it "hocus pocus on this parliamentary maneuver. People see through it."
He vowed that there were more than enough House Republicans who wanted to tie Obamacare defunding directly to the spending bill.
"It is important that we take a stand and put forward our priority which is delaying and defunding Obamacare," Michigan Republican Rep Bill Huizenga told CNN.
Huizenga said he's not satisfied with the current strategy on the bill, but said GOP leaders haven't reached out to him to explain why they think it's the best approach.
Senior House GOP leadership aides say they are still talking to members who just returned from a five-week recess about the details of their plan and feel confident that they will pull together the votes by next week.
But those efforts are complicated by several conservative outside groups pressuring House Republicans to vote against the bill and demand a showdown with Democrats over health care funding.
House GOP leaders can't count on much help from House Democrats. The Republican bill takes into account the mandatory and sweeping federal spending cuts that took effect in March that were required under a 2011 budget deal. Democrats oppose that, insisting on higher spending levels for domestic programs.
"I am not going to vote to continue the sequester," the No. 2 House Democrat, Steny Hoyer, told reporters on Tuesday, arguing the level set in the bill was "totally unacceptable and irresponsible."
There are currently 233 House Republicans so GOP leaders can only afford to lose 17 votes in order to pass the procedural vote to bring up the spending bill.
Republicans want to avoid a protracted fight over spending that would mean different versions of the government funding bill going back and forth between the House and Senate.
They are concerned that that forced cuts would ultimately be dropped in negotiations over the measure with the Senate.
"The sequester would never survive if we ping-pong this," one senior House GOP aide told CNN.
Senate Majority Leader Harry Reid requested a meeting with top congressional leaders to discuss fiscal issues.
On Thursday morning, Reid is scheduled to huddle with House Speaker John Boehner, House Democratic Leader Nancy Pelosi and Senate GOP Leader Mitch McConnell in Boehner's office.