President Trump stepped up his advocacy for a new round of middle-class tax cuts Tuesday, gaining support from one key congressional Republican even as it became clear that most of the GOP was unaware of his plans.

"On this one, we’re doing a pure 10 percent tax cut for the middle class, in addition to what they’ve already gotten," Trump told reporters in the Oval Office, referring to a tax-cut plan of his own conception that has surprised his party.

“It's going to be a resolution," introduced this week or next, Trump said.

Trump's sudden push for a new round of tax cuts, to add to the historic overhaul he signed in December, has caught Republicans and Democrats off-guard, and many are weighing whether he is serious in his demand. For now, lawmakers are in recess for midterm election campaigns.

[Opinion: Trump's middle-class tax cut election surprise]

Trump added that a senior Republican lawmaker, House Ways and Means Committee Chairman Kevin Brady, R-Texas, was working hard on the resolution.

Brady’s office declined to comment on the resolution or Trump’s remarks, but did issue a separate statement committing to working on a new middle class tax cut in the next Congress, which starts in January. That plan’s contingent on Republicans maintaining control of Congress in midterm elections.

"We will continue to work with the White House and Treasury over the coming weeks to develop an additional 10 percent tax cut focused specifically on middle-class families and workers, to be advanced as Republicans retain the House and Senate," Brady, the top Republican tax policy maker in the House and author of much of last year’s tax reform law, said in a statement.

Brady’s statement echoed similar elaboration from the White House that it wanted the 10 percent cut as part of the 'Tax Reform 2.0' package, aimed at making permanent the temporary individual tax cuts passed into law as part of last year’s tax reform package. That package is not expected to be taken up by the Senate.

“Building on the economic success of Republican tax cuts, which the House recently voted to make permanent as one part of Tax Reform 2.0, President Trump is determined to provide further tax relief for middle-class families,” Brady said.

The House of Representatives, which constitutionally must originate new revenue proposals, technically comes into session on Friday. But that session is merely a procedural formality; a member of the chamber comes in to gavel the chamber in and out without any actual legislation scheduled to be introduced or debated. In order to advance the resolution, members would need to pause electioneering at the height of campaign season.

Over the weekend and into the early part of this week the president surprised everyone, including members of his own administration, by calling for a new, major tax cut prior to the midterm elections, though both chambers of Congress are in recess for campaign season until after the early November election. He then pulled back the timeline until the lame duck session of the current Congress, due to take place in November and December, though observers on both sides of the aisle see his statements as a campaign tactic rather than serious policy proposal.

The Senate could take up the 'Tax Reform 2.0' package that the House of Representatives passed in late September, but unlike last year's tax reform law, that package would require Democratic support in order to advance due to procedural hurdles. Senate Majority Leader Mitch McConnell has not scheduled a vote on the legislation.