But some Republican lawmakers are questioning the plans, threatening to trip up the momentum.

The House Ways and Means Committee, meanwhile, advanced that chamber's tax legislation on Thursday . The GOP aims to pass it out of the House next week.

On Thursday, the Senate unveiled its plan to broadly chop business and individual taxes , which largely overlaps with a House tax bill but contains several differences. Senators plan to mark up, or debate and amend, the proposal starting Monday.

Republicans just took their biggest steps yet toward tax reform, but the GOP faces challenges in its push to overhaul the American tax system this year.

After the Senate plan's release Thursday, Sen. Jeff Flake, R-Ariz., voiced fears about the effect of broad cuts on the national debt. The budget resolution approved by Congress allows it to pass a plan that adds as much as $1.5 trillion to federal budget deficits over a decade.

While the nonpartisan Congressional Budget Office has not scored the Senate plan, it estimated that an earlier version of the House bill would increase federal budget deficits by $1.7 trillion over 10 years.

The current plans appear to come nowhere close to canceling out tax cuts with new revenue.

"I remain concerned over how the current tax reform proposals will grow the already staggering national debt by opting for short-term fixes while ignoring long-term problems for taxpayers and the economy," Flake, who will not run for re-election next year, said in a statement. "We must achieve real tax reform crafted in a fiscally responsible manner."

Along with Flake, Sens. Bob Corker, R-Tenn., and John McCain, R-Ariz., have expressed concerns about ballooning the national debt. Corker, who will also leave the Senate, has previously said he would not vote for a tax plan that adds "one penny" to the deficit.

The CBO also projected that debt would rise to 97.1 percent of gross domestic product in 2027, up from 91.2 percent under current CBO projections.

The forecast did not include the estimated effects of economic growth. Republicans argue that growth sparked by the bill will help to offset, or cancel out entirely, the budget shortfall caused by broad tax cuts.

However, it is not clear if the tax cuts can spark the growth necessary to do so.

Meanwhile, two other GOP senators called for more changes to the child tax credit to further reduce the burden on middle-class taxpayers. The Senate plan would increase the credit from $1,000 to $1,650. Sens. Marco Rubio, F-Fla., and Mike Lee, R-Utah, on Thursday called for a $2,000 credit.

"We continue to believe that the best way to provide real relief to working families is through a straightforward, significant, and permanent expansion of the child tax credit — preferably doubling the credit to $2,000 per child and expanding its applicability to payroll taxes," they said in a statement. "The Senate is not going to pass a bill that isn't clearly pro-family, so we look forward to working with our colleagues to get there."

Sen. Rand Paul, R-Ky., has previously called for even deeper tax cuts.

The GOP, which holds 52 seats in the Senate, is working on a tight margin to pass a bill. Republicans can only lose two votes.

Meanwhile, in the House, Republicans can lose just 22 votes to still pass a plan.

The proposal's fate in that chamber may hinge largely on how a bill treats state and local tax deductions. Many Republicans — enough to sink legislation on their own — represent districts in high-tax blue states, which benefit from the provision. They have expressed concerns about eliminating those deductions.

The House bill changes the provisions to allow taxpayers in those states to deduct up to $10,000 of property taxes. The Senate bill scraps all state and local deductions.

No GOP senators represent the states that benefit most from the deductions, like New York, California and New Jersey.

If the House and Senate pass separate bills, they will have to reconcile them before approving a final bill. Agreeing on the state and local measures could prove contentious at that time in the negotiations.

Republicans, who have long sought to trim corporate and individual taxes to spark economic growth, see passing a tax plan as critical to their electoral chances in the 2018 midterms.