Updated at 8:48 p.m. ET Senate Republicans ran into a speed bump Thursday evening in their quest to pass a tax overhaul by the weekend, over concerns that the bill could fall far short of GOP promises of economic growth.Deficit hawks threatened to abandon the legislation over those concerns, sending leaders back to the drawing board to find ways to scale back the cost of the $1.4 trillion tax plan. The fight over the long-term cost of the tax overhaul could force leaders to scale back plans for permanent corporate rate cuts, greatly reducing the ambition of the tax overhaul.Progress on the bill ground to a sudden halt on Thursday evening after deficit hawks received word that their back up plan to keep the cost of the legislation under control would violate Senate budget rules. Senate Republican Conference Committee Chairman John Thune, R-S.D., told reporters Thursday that leaders were attempting to rework a plan appease a small group of Senators — including Republican Sens. Bob Corker of Tennessee, Jeff Flake of Arizona and Ron Johnson of Wisconsin — who want assurances that the bill won't add to the deficit in the future. "It's kind of a bit of a moving target," Thune said. "Hopefully they're going to get an agreement here pretty soon."The trio of deficit hawks balked after it became clear that Senate budget rules wouldn't allow a trigger mechanism that would roll back some tax cuts or impose some spending cuts in the future to keep the deficit under control. Floor action stalled for about an hour on Thursday evening as senators huddled with the Senate parliamentarian. Walking out of that huddle, they believed the trigger mechanism would not fit Senate rules.Instead, leaders are now discussing a plan that could gradually reduce some of the tax cuts laid out in their plan. Sen. John Cornyn of Texas, the No. 2 Republican in the Senate, said other options were being discussed. The possibility under consideration now is fixing a date at which tax rates would increase, possibly in a gradual fashion, unless Congress acted again. But figuring out how to divide those eventual increases between the individual and corporate sides of the tax code remains uncertain."I think they could probably do something six years out, it would go up about half a percentage point," Cornyn said. "I think what they're talking about is some sort of stair-step."Sen. David Perdue, R-Ga., described the idea as "intense stimulus now, less intense stimulus later." Perdue says it's unlikely that a new package would be seen Thursday night, but he still thinks final passage is possible Friday.The parliamentarian's decision deepened frustration among Republicans following a new report from the Joint Committee On Taxation found that that the tax cuts would not pay for themselves. The updated reportfound that the tax cuts would only generate about a third of the economic growth that Republicans expected. Many Republicans rejected the report, saying the estimate was based on incomplete data. "I believe it's clearly wrong," Cornyn told reporters. "But that's just my opinion."NPR's Scott Detrow and Arnie Seipel contributed to this report. Copyright 2017 NPR. To see more, visit http://www.npr.org/.