Sen. Lindsey Graham Lindsey Olin GrahamMomentum growing among Republicans for Supreme Court vote before Election Day Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Warning signs flash for Lindsey Graham in South Carolina MORE (R-S.C.) is warning that his party needs to make good on their years-long campaign promises or prepare to lose in 2018.

"We're going to succeed together or we're going to fail together. If we don't cut taxes after all these years of promising then I think the party comes unraveled," Graham told reporters Tuesday.

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He added that if Republicans don't pass a tax plan or repeal ObamaCare "eventually in these primaries against senators — we're going to start losing these primaries, and the biggest loser in all this would be President Trump."

Graham's comments come as Republicans are starting debate on a budget that includes instructions allowing them to avoid a Democratic filibuster on their tax plan.

Though Republicans are still in the early stages and don't yet have a bill, there are early signs of trouble in their quest to get 50 votes.

"If we don't produce the party is over for Republicans. ... If you care about the Republican Party we better produce because those who put us here have had it with us," Graham added.

Republicans face a favorable map in 2018, where Democrats are defending 25 seats including 10 in states won by President Trump.

But the party is facing a growing slate of nasty primary fights as anti-establishment candidates, in part backed by former Trump adviser Stephen Bannon and his allies, are planning to challenge GOP incumbents.

Graham added the best antidote for Bannon would be the Senate passing major legislation.

"If we go into 2018 saying 'well, we just don't have enough Republicans' Bannon will beat them all or come close to beating them all because he's tapped into frustration," Graham added.

Trump has also lashed out at several GOP senators, including Sen. John McCain John Sidney McCainMomentum growing among Republicans for Supreme Court vote before Election Day McConnell urges GOP senators to 'keep your powder dry' on Supreme Court vacancy McSally says current Senate should vote on Trump nominee MORE (R-Ariz.) on Twitter on Tuesday. The attacks have at times sparked frustration from GOP senators, who want the president to focus his fire on Democrats.

Graham, who is close with McCain, said that his "advice to the president, and really to all of us, is focus on what we have in common."