President Trump will dine with six key senators — three Democrats and three Republicans — at the White House Tuesday night, as his administration endeavors to overhaul the nation's tax code.

Sen. Joe Donnelly, D-Indiana; Sen. Heidi Heitkamp, D-North Dakota; Sen. Joe Manchin, D-West Virginia; Sen. Orrin Hatch, R-Utah; Sen. Patrick Toomey, R-Pennsylvania; and Sen. John Thune, R-South Dakota, are the attendees, the White House has confirmed to CBS News. As the White House tries to steer Congress' attention towards tax reform, other administration controversies -- like the president's decision to end the Deferred Action for Childhood Arrivals (DACA) program for young immigrants and move to side with Democrats on extending the debt ceiling -- have forced Congress to divide its attention. Republicans are also looking to make a last-ditch attempt on health care, with four GOP senators planning to introduce a measure Wednesday to repeal and replace Obamacare.

Mr. Trump's sudden alliance with Democrats over his own party on extending the debt limit for three months — coupled with his recent harsh criticisms of Senate Majority Leader Mitch McConnell, Speaker of the House Paul Ryan and other GOP leaders — may be an indication that he will be more open to working with Democrats in the future on issues like tax reform.

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A White House official told CBS News the president is committed to passing tax relief for the middle class, and is willing to work with both parties to accomplish that. Donnelly, Heitkamp and Manchin were the only three Democrats who did not sign a letter from Senate Minority Leader Chuck Schumer last month outlining Democrats' must-haves for tax reform.

In a recent speech in Missouri, Mr. Trump outlined the main goals for any tax reform — simplifying the tax code, eliminating loopholes for special interests, giving lower taxes to the middle class and slashing the corporate tax rate. Then, Mr. Trump urged Congress to "at least try to put the partisan posturing behind us and come together as Americans" on tax reform.

Republicans must start the Tax Reform/Tax Cut legislation ASAP. Don't wait until the end of September. Needed now more than ever. Hurry! — Donald J. Trump (@realDonaldTrump) September 8, 2017

Mr. Trump has urged Republicans to "hurry" and reach a deal on taxes as soon as possible. The White House has never released a fleshed-out plan for its tax reform goals, leaving many of the details to Congress.

CBS News' Jillian Hughes contributed to this report.