After conservative defections, House Republican leaders have delayed a vote on a bill to avert a government shutdown, saying that they need more time to build support for the proposal.

The bill, which would fund the government until mid-December but would also include a provision to defund the Affordable Care Act, has exposed a strategic rift between GOP leadership and Tea Party-affiliated Republicans who want ‘Obamacare’ gutted even if it risks a government shutdown.

Some in the leaders’ camp are growing frustrated with the strategy by the party’s most fervent anti-Obamacare wing, saying that the movement’s leaders in the Senate have not come up with a better plan than their proposed coupling of the government funding bill with a defunding of the President’s signature legislative achievement.

“Does Ted Cruz have a plan to get 41 votes? Does he have a strategy he's executing on to get 41 votes? Not that I'm aware of,” a GOP leadership aide told NBC News, “Has he ever come to the House leadership and said, ‘Here's my plan to get 41 votes in the Senate, to hold the line so we can defund Obamacare?’ Never. No. He's just on his twitter account attacking House Republicans.”

The GOP leaders’ strategy to combine the two measures is intended to force the Democratically-led Senate into a politically dicey vote on the health care’s defunding. Conservative Republicans say that plan is merely a “gimmick” because the Senate could still strip out the health care provision and vote only on the government funding piece of the bill. They say they want legislation that would bind both measures together, making avoiding a government shutdown contingent on gutting the 2010 Obama health law.

Conservative Republicans in the House are plowing ahead with their opposition of the plan, and keeping a tally of those who are leaning in their direction. Freshman Republican Rep Thomas Massie, R-Ky., told reporters today that he has a list of between “50 and 80” Republicans who plan to vote against it, far more than would be needed to derail the bill. A GOP Leadership aide told NBC News that count “is not correct,” but would not say how close, or far, Massie was from their own estimate.

Rep Tim Huelskamp, R-Kan., told reporters Tuesday that the plan by Republican leadership was “to just give up on Obamacare, pat people on the head and say, 'We had your vote, you had your vote, it didn't count.'"

"It doesn't count, it has no impact whatsoever on any policy, it's just another vote and that's insufficient for my folks when I went home and told them I'm going to do something," Huelskamp continued.

Conservative groups like the Club for Growth and Heritage Action lobbied Republicans to vote against the GOP plan this week, and warned that their political advocacy arms would hold them accountable for supporting it.

But that strategy from outside groups has rankled some who don’t want to be held responsible for shutting down the government if the strategy doesn’t work.

“Occasionally we do disagree on tactics and this is one where I do disagree,” Rep Tom Cole, R-Okla., said of Club for Growth encouraging members to oppose the measure introduced by Republican leadership, “Their idea is to use our majority to try to accomplish the aims of a minority of their minority, and that to me is sort of backwards.”

The bill to temporarily fund the government past September 30 was originally slated for a vote as early as Thursday. Aides now say they plan to consider the bill next week.

Republican leadership aides say that they had anticipated trouble with selling the relatively complicated legislative strategy to members, especially in the wake of briefings and debate related to Syria. GOP staff members had stressed all week that they planned to consider this legislation "as early as Thursday."

The bill will likely have to pass with only Republican votes after Democratic leaders said that they oppose the GOP proposal, in part because it would maintain the spending levels put in place by the across-the-board budget cuts known as sequestration.

Carrie Dann contributed