According to Sunday reports, a dozen Republicans in blue states may vote against Tax Reform 2.0.
"Passage is not automatic", he added.
"Anytime we're talking about tax cuts and the growing economy, we're winning", said Matt Gorman, a spokesman for the National Republican Congressional Committee, the party's main campaign support for House Republican candidates.
Though this is planned by the Republican lawmakers, several lawmakers from high-tax states disapprove of some provisions, especially due to the fact that Tax 2.0 included state and local tax (SALT) deduction cap.
Even if the initiative fails to pass, it could put Democrats in the position of opposing the new tax-cut plan on the House floor, which Republicans could seek to use to their advantage in the November 6 elections where control of Congress will be at stake.
Experts claim the rule affects high-tax states like California, New York and New Jersey - all which have highly contested midterm races.
The legislation would make permanent last year's tax breaks for individuals, preventing them from facing a tax increase in eight years, while boosting incentives for retirement savings and giving more lenient tax treatment to startups and small businesses.
Booming sales for Woodward's 'Misfortune,' Trump presidency guide
As such, various liberal and conservative commentators called out Eric Trump for his comments in that interview. Donald Trump himself has repeatedly lashed out at Woodward as well.
Republicans say the legislation will also seek to encourage start-up businesses by allowing them to write off more start-up costs and add investors without limiting tax benefits, such as research and development credits.
To the dismay of party leaders, the healthy economy and Trump have become countervailing forces.
While the law slashed the corporate tax rate permanently from 35 percent to 21 percent, its tax cuts for individuals and the millions of US "pass-through" businesses expire in eight years.
That message was supported on Wednesday by separate data that showed the national median income a year ago - Trump's first in office - rose to its highest in a decade after adjusting for inflation and survey changes.
If that happens, it would be the first time since 2012 the USA economy would have to support such a large deficit, highlighting a basic shift for the Republican Party, which once prided itself on fiscal conservatism.
Trump is touting the positive impact of tax cuts on jobs and the economy as he campaigns for Republicans ahead of the 2018 midterm elections. Obama, who saw GDP growth of just over 1 percent, doubted that Trump could achieve 4 percent expansion. But as Trump's populist attacks against free trade have erupted into trade wars with China and USA allies, trade tensions have overshadowed the tax cuts in economically vulnerable areas of the country that depend on exports. "Still plenty to do!"