The Republican bill was approved on a 227-203 vote, with no Democrats supporting it.
But Democratic challenges could still provide some drama - or at least, a brief delay - after the bill heads to the Senate.
The bill also matches the version passed by the Senate in doing away with the Affordable Care Act's individual mandate to obtain insurance, effectively making the tax bill double as Republicans' biggest blow to Obamacare.
To clear the House, the GOP tax bill must receive a simple majority, which would be 2018 votes. The delay would be only temporary. The cap remains in the final bill. "We're still talking to the parliamentarian about that", Cornyn said, referring to the Senate adviser on rules and procedures. "We know in this country that we're not reaching our potential. But that's what this process is created to tell us".
Rohrabacher is still a "no", according to Bloomberg News, but there will be sufficient votes to allow the bill to pass the House. Jeff Flake (R-Ariz.) meanwhile, appears to be the only undecided Republican, and even if he votes against the bill, Vice President Mike Pence would cast a tie-breaking vote to pass the bill. But either side can elect to give up some of its time, and Republicans may do so to speed passage.
"A mixture of theology and science fiction" is how Representative Richard Neal of MA, the ranking Democrat on the House Ways and Means Committee, described the Republicans' bill. Neal cited the fast pace of the legislation - which was introduced in the House a little over six weeks ago - as one of the reasons for future fixes.
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"For a lot of folks its going to be the Democrats who get the luxury - just as Republicans have had for awhile with President Obama - of just saying 'No, everything is bad.' And unfortunately that sort of fits the mood of the country", said McHenry.
Ways and Means Chairman Kevin Brady acknowledged future work to be done on the US tax code, including changes to retirement savings and tax provisions for start ups. "I think there are various ways to improve this". Marco Rubio of Florida and Bob Corker of Tennessee.
"This is America's comeback", added number two House Republican Kevin McCarthy.
Despite many state residents' concerns over losing the full deductibility of local and state taxes and lower mortgage tax deduction limits, 12 Republican representatives from California voted in favor of passing the bill.
Rep. John Faso, an upstate New York Republican who voted against the bill Tuesday, said in a Monday statement that the change in the SALT deduction "will accelerate the trend of hardworking individuals and businesses already leaving our state - further eroding New York's tax base". The largest cuts would go to the wealthy, but, in 2018, almost all Americans will see their income tax go down, according to a nonpartisan analysis of the final plan released Monday.
Still, there are dissenting Republicans in the House. The aid likely would be attached to a government spending bill that must be passed this week to keep the government open after Friday. "The Senate will still vote tonight, and the House will vote tomorrow to send the final bill to the President's desk".
The tax bill would lower taxes on average across the income spectrum for the first eight years, with the largest benefits going to upper earners, according to a new analysis by the Urban-Brookings Tax Policy Center. For example, in a previous version of the GOP tax bill, graduate students were up in arms because tuition wavers were slated to be taxed. The top 1 percent would get $51,140 on average, and the top 0.1 percent would get $193,380, it found.
"Stocks and the economy have a long way to go after the Tax Cut Bill is totally understood and appreciated in scope and size", he added in a separate tweet. Though there are still seven brackets, the tax reform bill changes the rates paid by filers in each bracket, dropping the rates by as much as 4%.