(CNN) President Donald Trump suggested to House Republicans at a bipartisan meeting on tax reform that if they fail to act on health care, he would work with Democrats instead, issuing a loaded warning on a topic that's seen little to no cooperation between the two parties.

Trump made his threat as members of the House Ways and Means Committee met Tuesday with the President at the White House to discuss an entirely different topic: tax reform.

According to members who attended the sit-down, Trump stressed that he wanted a bipartisan effort on tax reform and expressed frustration with his own party for failing to pass a health care bill.

Just hours later, Senate Republicans announced they would not hold a vote on the latest iteration of their health care bill, marking yet another failed attempt to repeal and replace the Affordable Care Act.

Trump told the group at the White House he was "disappointed" in Republican senators who came out against the recent Graham-Cassidy bill and doomed its prospects, according to Democratic Rep. Linda Sanchez, who was at the White House meeting.

Sanchez said Trump "chided" the Republican members in attendance, saying he could end up working with Democrats on health care legislation.

"We'll see if that happens," Sanchez said, adding that it wasn't a long discussion.

Rep. Richard Neal, the top Democrat on the Ways and Means Committee, described the President's tone as "less than strident" but said "he made that clear that if he didn't get what he wanted, he was going to work with Democrats on a plan."

New York Republican Rep. Tom Reed who attended the White House meeting Tuesday told CNN he didn't classify the comment from the President as a "threat," but said the President "wants to govern for the American people and if there are folks on our side who just cannot get to that point than obviously you have no alternative but then to work with folks on the other side who will be good faith negotiators."

"There was definitely a clear signal that he's willing to work with legislators who want to govern and I support that wholeheartedly," said Reed, the co-chairman of the group known as the "problem solvers caucus."

Goals for tax reform revealed

The bipartisan meeting came one day before Republicans are set to unveil a framework of their tax reform plan.

Trump reiterated that the plan would be "middle class tax cut" and said there would be no tax cuts on the wealthy, according to Republican Rep. Jim Renacci of Ohio.

Trump was "pretty adamant" about wanting to get tax reform done, Renacci said, adding that the President was also passionate about a child care tax credit proposal being pushed by his daughter, Ivanka Trump.

"He wants to make sure that the credits are to a point where single working mothers and fathers can be able to afford childcare while they're working," Renacci said.

Neal, who took notes during the meeting, showed reporters his notepad with a quote that he wrote down, saying it was from Trump: "The rich will not benefit." It's a promise that Democrats are planning to keep in the spotlight as the tax reform debate continues.

While Trump has repeatedly said his tax plan wouldn't benefit the wealthy, Neal said that Trump was prepared to move forward with repealing the estate tax -- which affects estates worth more than $5.49 million -- and indicated that lowering the top individual income tax rate was negotiable.

Two Republicans familiar with the plan expect the top income rate will drop to 35% from 39.6%, and the top corporate rate will drop to 20% from 35%. But Republicans working on the plan stress that the rates are still fluid and could change before the release of the framework Wednesday.

Democrats argue that a drop in the individual top rate would be a tax cut for the wealthy.

"We want the top rate to stay at 39.6%," Neal said. "It sends the signal that they're entirely true to the statement that was made on the campaign trail, that they intend not to offer any tax relief to the people at the top."

But even if the rate does decrease, it's not clear yet whether the richest Americans would pay less in federal income taxes overall because other changes could be made in the tax code that could offset the benefits they receive from a lower rate.

Trump is expected to address the plan Wednesday in an Indiana speech, while House Republicans will gather for a retreat to discuss some of the details.