Rep. Louie GohmertLouis (Louie) Buller GohmertGOP lawmaker calls for Mueller to be fired in speech on House floor GOP lawmaker calls for Mueller recusal over uranium deal Overnight Finance: Freedom Caucus chair courts Dems on tax reform | House passes .5B disaster relief package | House GOP worries about budget's fate in Senate MORE (R-Texas) said Tuesday that the Republican leadership is "scared to death" of efforts to block funding for ObamaCare, fearing the strategy could end the GOP's House majority.

"They think if we have a shutdown, or a big showdown, we may lose the majority, and they will lose their leadership positions," Gohmert said at an event in Longview, Texas, according to the Longview News-Journal.

Gohmert said Republicans need to stand up for what they believe in — as Democrats did when they passed the president's healthcare reform law — and now push to defund it.

"What does it say about Republicans if we're not willing to stand up for what we know is best for the country?" he asked.

Gohmert and other Republicans in the House and Senate have said they will push to defund ObamaCare as part of the continuing spending resolution for 2014. But many GOP lawmakers fear the party will be hurt if the strategy ends in a government shutdown.

Many Republicans see President Obama's decision to delay the employer mandate for a year, and other delays to the law, as a reason to defund the entire law as part of the 2014 spending deal.

Others, however, say the GOP should be pushing for a broad, one-year delay of the law. Rep. Tom Price (R-Ga.) told The Atlanta Journal Constitution on Tuesday that the GOP should work quietly with Democrats to engineer a delay.

"[I]f you take any one component out of this, the whole thing doesn't work," Price said. "The delay for a year is a solution."