In interviews, several House members who speak to Lee, Cruz and other senators such as Rand Paul (R-Ky.) and Marco Rubio (R-Fla.) on a regular basis, described the conservative faction’s double-barreled philosophy: Use their influence in the House majority to steer leadership toward conservative goals like defunding Obamacare in spending bills while right-wing all-stars like Cruz use the Senate floor as a national press platform.

“We feel like we can be more effective that way. They’ve got bigger bullhorns [in the Senate] where they can drive the message across the country through the media,” said Rep. Marlin Stutzman (R-Ind.). “And in the House, we’ve got the majority. I think it makes a good team at the end of the day.”

Senior Republican aides in both chambers — often furious with the scheming of the new brand of congressional Republicans — describe the relationship between the right flanks in the House and Senate as dictatorial. They argue Cruz and Lee come over to the lower chamber and deliver legislative marching orders that are difficult to achieve, like insisting on defunding the president’s primary legislative achievement. Democrats are quick to seize on that tension, urging that “reasonable” Republicans show some courage and stand up to the right and joking of a “Speaker Cruz” pulling the strings in the House.

House conservatives dispute this dim view of the congressional GOP’s intraparty relations.

“People believe that they come and try to influence the House of Representatives. These are folks that are on the Senate side that we have invited over to speak with us,” said Rep. Jim Bridenstine (R-Okla.). “That’s perfectly appropriate. And we all had one goal. One: fund the government. Two: protect our constituents from the harmful effects of Obamacare.”