Representative Chip Roy of Texas was sitting in a suite in the speaker’s office at the Capitol on a wintry afternoon last December, laying out why he could not possibly support a year-end spending bill that would suspend the federal debt limit, when President Trump’s threat came through.

“The very unpopular ‘Congressman’ from Texas, Chip Roy, is getting in the way, as usual, of having yet another Great Republican Victory - All for the sake of some cheap publicity for himself,” Mr. Trump wrote on his social media site. “Republican obstructionists have to be done away with.”

It was not the first time that the president had called for his ouster, but Mr. Roy was unbowed.

Not long after, he strode to the House floor to deliver a scathing speech against the legislation Mr. Trump was pressing him to support, a move that foreshadowed the clash currently playing out, as Mr. Roy resists pressure from the president to fall in line behind his marquee domestic policy package.

“To take this bill yesterday and congratulate yourself because it’s shorter in pages, but increases the debt by $5 trillion, is asinine,” Mr. Roy said in December. “I’m absolutely sickened by a party that campaigns on fiscal responsibility and has the temerity to go forward to the American people and say you think this is fiscally responsible.”

That same ideology is driving Mr. Roy as he leads a faction of right-wing holdouts pushing for substantial changes to what Republicans call their “big, beautiful bill” of tax and spending cuts, arguing that it would add far too much to the already soaring federal debt. They are a key reason that Speaker Mike Johnson has been unable to cobble together the votes to pass the package.

Whether Mr. Roy will dig in against the package or relent — as he often has after threatening to tank a key party priority — could determine the fate of the entire effort.