Sen. Bob Corker. Mark Wilson/Getty Images After multiple failed ventures on healthcare overhaul, President Donald Trump and Republican lawmakers are under more pressure than ever to deliver a legislative victory and fulfill a significant campaign promise.

But even with the political momentum, getting tax reform through the Republican-controlled Congress already faces some stumbling blocks. One big hurdle could be the possibility that the GOP's latest tax plan would significantly increase the deficit, Sen. Bob Corker of Tennessee said Sunday during an appearance on NBC's "Meet the Press."

"But if it looks like to me, Chuck, we're adding one penny to the deficit, I am not going to be for it, OK?" Corker told host Chuck Todd. "I'm sorry. It is the greatest threat to our nation. The greatest threat to our nation."

Corker last week said he would not seek reelection next year.

An analysis from the Tax Policy Center found that the tax framework released last week would add $2.4 trillion to the deficit over a decade.

Part of the concern about the deficit could be alleviated by the Trump administration's use of what is known as dynamic scoring, which assumes increased tax revenue based on expected economic growth from tax cuts — though many economists have questioned the practicality of the concept.

Gregory Daco, the chief US economist at Oxford Economics, said the success of the plan would come from how Republicans were "able to present this tax proposal."

Daco told Business Insider:

"Now, we know on the Senate side, Republicans have supported a budget resolution that would allow for $1.5 trillion worth of deficit-increasing measures. So there's indeed some increased tolerance for some increase in the federal deficit, and I think we're going to see that shift away from no increase in the deficit to some tolerance for a modest increase in the deficit. And add to that some dynamic scoring ... and you might have greater tolerance for a plan that might not increase the deficit — at least not on paper — that substantially."

Chris Krueger, an analyst at Cowen Washington Research Group, said Corker could be just the start of Republican leaders' worries in the Senate.

For one, using budget reconciliation to try to pass a tax-reform bill could lead to the same concerns that prompted Sen. John McCain to vote against various GOP healthcare bills — and McCain has a history of raising concerns with tax proposals.

"We would also note Sen. John McCain's comments about regular order — and that he voted against the Bush 2001 tax cut for Corker-esq reasons," Krueger wrote in a note to clients on Monday. "If you lose Corker and McCain, the margin for Senate error is zero.

"Add in Sens. Susan Collins, Rand Paul, etc., and you can see the problems with the voting arithmetic — to say nothing of the policy arithmetic ... which is far more difficult," Krueger said. Republicans hold 52 seats in the Senate.

There are also questions about whether more hardline deficit hawks in the House would go along with a plan that is projected to add trillions to the country's debt. The conservative House Freedom Caucus on Wednesday said it supported the framework, but with significant changes expected during the process of turning it into a bill, it remains to be seen if that will hold.