Freshman Rep. Jim BridenstineJim BridenstineLawmakers sound alarm on space security The Hill's Whip List: 36 GOP no votes on ObamaCare repeal plan A guide to the committees: House MORE (R-Okla.) said Tuesday that he fears Republicans, and Speaker John BoehnerJohn Boehner6 reasons 'TrumpCare' flatlined Paul Ryan sells out conservatives with healthcare surrender Matt Schlapp: 5 lessons Trump, Ryan must learn from healthcare debate MORE (R-Ohio) in particular, will cave in and accept a tax hike once the sequester hits in March.

"My concern, and I think the concern of a lot of Republicans in Congress, is that once the sequester takes effect, people are going to be screaming for a deal, and that deal ultimately is going to be what the president wants — to raise taxes," Bridenstine said, according to the Tulsa World.

"And if there's enough pressure, [BoehnerJohn Boehner6 reasons 'TrumpCare' flatlined Paul Ryan sells out conservatives with healthcare surrender Matt Schlapp: 5 lessons Trump, Ryan must learn from healthcare debate MORE] will bring it to the floor and 200 Democrats and 30 or 40 Republicans will vote for it," he added. "And once again you have the Speaker caucusing with the Democrats."

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Bridenstine said Republicans are already "caving too much" on the budget.

"My beef is that we're caving too much," he said. "If everything you do is what the president wants, then there is no compromise."

Bridenstine started the year by sounding a critical note on Boehner as one of the 12 Republicans who didn't vote for Boehner for Speaker. He and two other Republicans voted for Majority Leader Eric CantorEric CantorPaul Ryan sells out conservatives with healthcare surrender A path forward on infrastructure Democrats step up calls that Russian hack was act of war MORE (R-Va.).

"There are probably a lot of freshmen he doesn't know the names of," Bridenstine said. "He pays a lot of attention to me, and the reason is because I stood up to him on something."

Congress returns next week and faces a four-day deadline to either reach a deal on the sequester, or watch it take effect on March 1. The sequester would cut $85 billion in defense and non-defense discretionary spending in 2013.

Before the House left last week, Boehner said the chamber would not pass anything on its own to avoid these cuts, and would only look at legislation that the Senate passes. Senate Democrats have proposed a bill that replaces half of the sequester with tax increases, something that is unlikely to move in the House.