And moderates are increasingly tiring of it -- especially after Tuesday's repudiation of a candidate seen as emblematic of the GOP's right flank in the Alabama special election.
Government funding and efforts to abolish Deferred Action for Childhood Arrivals, a popular program for young undocumented immigrants, have some moderates increasingly wondering: Why can't we play hardball, too?
Moderate Republicans and House members in districts that are either generally competitive or which Hillary Clinton carried in the 2016 presidential election are starting to grow frustrated with the effectiveness of groups like the House Freedom Caucus in influencing legislation, often by withholding their votes as a bloc until demands are met.
"Yes," Florida Republican Rep. Carlos Curbelo said with exasperation when CNN asked Wednesday if the time had come for centrists to borrow tactics from the far right.
"We cannot be spectators here," Curbelo said. "Other groups have used their leverage to influence the process, and we must do so as well, especially when there are 800,000 lives which could be radically changed for the worse if we don't take care of (DACA)."
"I think last night's election's going to cause a lot of people to re-think where we are and what we're doing," said New York Republican Rep. Pete King of Democrat Doug Jones's victory in Alabama.
While the current focus is on passing tax reform, one Republican staffer said patience could be limited once it's dispensed with, as vulnerable moderates are frustrated with being forced to take tough votes seen in many cases as messaging exercises to appease the conservative base.
"It's the moderates who are going to have to run in tough elections on this sh**," the staffer said.
But there remains skepticism that, despite the frustration, moderates can hold together as a group the way conservatives have been able to do, or are willing to stomach the tough tactics the right flank employs.
The conservative House Freedom Caucus, for example, almost tanked a procedural measure on tax reform in a public show of force on the House floor earlier this month to send a message to Speaker Paul Ryan about year-end funding.
And according to a Republican source, rumors have been building around the Capitol that the farther right lawmakers are prepared to challenge Ryan's speakership immediately if he calls a stand-alone fix for DACA to the floor.
Nearly three dozen moderates, on the other hand, sent a carefully worded letter to Ryan urging him to move on a fix for DACA, which protects young undocumented immigrants brought to the US as children, by the end of the year, without making any concrete threats to withhold any votes on government funding.
Curbelo has committed to oppose government funding without clear progress toward a DACA fix, and is urging fellow Republicans to do the same.
Pennsylvania Rep. Charlie Dent, a moderate Republican who has decided to not seek reelection, said he agreed with Curbelo that a DACA fix should go on an upcoming must-pass bill, though it could potentially be in January.
"The power of 25 here can force a lot of things," Dent said, referring to the GOP margin of the majority in the House. "And Freedom Caucus has been effective at it, they can put their votes together, and we need to do that from time to time, (though) we need to pick our fights carefully."
But one conservative Republican source noted that moderates have always had difficulty being as united as more conservative groups. That sentiment was echoed by King, who referred to the group that former House Speaker John Boehner once called
"legislative terrorist(s)" as "crazies" even as he distanced himself from moderates.
"I consider myself actually a blue-collar conservative, I'm not really in the moderate wing, I'm just against some of the crazies," King told CNN, speaking of his unsuccessful fight against the GOP tax bill he sees as devastating for his state. "It's hard to unify everybody."
Some moderates gave credit to the Freedom Caucus, saying their effectiveness should only be a source of inspiration.
"I don't fault anybody for doing what they believe is best in their way of representing their district," said Washington Rep. Dan Newhouse, who helped organize the DACA letter. "I respect that. ...(But) it's also incumbent upon me to do the same thing."