Story highlights Cruz is widely expected to run again for president in 2020 if Donald Trump loses a general election match-up

If Trump loses, Cruz could make the case that the outcome would have been far different with him as the nominee

Washington (CNN) Texas Sen. Ted Cruz promised his party Tuesday that he is "not suspending our fight for liberty."

And that is precisely what many Senate Republicans fear.

As he returns to Capitol Hill after ending his presidential campaign, Cruz has grown more powerful and influential with core GOP voters, giving him a major platform to upend his party leadership's most carefully constructed plans. And as Congress prepares to deal with major national issues -- including a rescue plan for Puerto Rico requiring immediate action and government funding in the fall -- many believe Cruz could use his new bully pulpit to wreak havoc on Capitol Hill should he want to.

With Cruz widely expected to run again for president in 2020 if Donald Trump loses a general election match-up with Hillary Clinton, the Texas freshman could once again use his fights with Senate Republicans as the basis of his run. And that is enough to unnerve many Republicans.

Asked about Cruz over the next four years, retiring Indiana Sen. Dan Coats -- a leading Cruz critic -- said: "All I know is I won't be here to enjoy the theater."

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