House Ways and Means Committee Chairman Kevin Brady Kevin Patrick BradyBusinesses, states pass on Trump payroll tax deferral Trump order on drug prices faces long road to finish line On The Money: US deficit hits trillion amid pandemic | McConnell: Chance for relief deal 'doesn't look that good' | House employees won't have payroll taxes deferred MORE (R-Texas) said Tuesday that he expects the House to vote on a second round of tax cuts in September.

"We anticipate the House voting on this in September and the Senate setting a timetable as well," Brady said in remarks from the White House, where he and other GOP members of the committee met with President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE.

A September vote would allow the House to take up the tax package just weeks before the midterm elections.

Republicans hope to use a tax vote to help their members, and many of the Republicans attending the event at the White House face competitive races this fall.

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Lawmakers who attended the meeting included Rep. Diane Black Diane Lynn BlackBottom line Overnight Health Care: Anti-abortion Democrats take heat from party | More states sue Purdue over opioid epidemic | 1 in 4 in poll say high costs led them to skip medical care Lamar Alexander's exit marks end of an era in evolving Tennessee MORE (R-Tenn.), who is running for governor, Rep. Jim Renacci James (Jim) B. RenacciOhio is suddenly a 2020 battleground Democrats fear Ohio slipping further away in 2020 Medicare for All won't deliver what Democrats promise MORE (R-Ohio), who is running for Senate, Rep. Mike Bishop (R-Mich.), who is seeking re-election in a race the Cook Political Report calls a toss-up, and Rep. George Holding George Edward Bell HoldingGOP lawmaker says US-UK negotiators working 'fast and furious' on trade deal Hispanic Caucus campaign arm endorses slate of non-Hispanic candidates Whiskey, workers and friends caught in the trade dispute crossfire MORE (R-N.C.), whose re-election race is rated "likely Republican" by Cook.

The focus of the tax package is expected to be a permanent extension of the tax cuts for individuals that were a part of the tax law Trump signed in December. Brady said that he thinks it's important to cement the tax cuts so that Democrats can't reverse the benefits for middle-class taxpayers in the future.

"We can protect them against a future Washington trying to steal back those hard-earned dollars that you and Republicans in Congress has given them," Brady said to Trump.

While a bill to cement the individual tax cuts is likely to pass the House, it would face challenges in the Senate, where it would need some Democratic support. There also are some Senate Republicans who are reluctant to vote for another tax-cut bill if it would further add to the deficit.

Still, House Republicans see benefits to holding a vote on another tax bill in order to highlight their 2017 tax bill and to put Democrats on the spot. They also think that there are policy benefits to making the individual tax cuts permanent, with Brady saying that doing so would help to create more jobs.

Brady's comments about the tax cut 2.0 efforts came after Trump spoke about his meeting and press conference with Russian President Vladimir Putin.

Brady said that "peace through strength is foreign policy that works, and it works best when America has a strong economy and a strong military."