Washington (CNN) President Donald Trump told Republican senators lunching at the White House Tuesday the House-passed health care reform bill he celebrated earlier this year was "mean," a source told CNN.

Trump made clear multiple times that he was pleased that the Senate negotiations appeared to be moving away from where the House version of the repeal and replace effort ended up, according to three sources familiar with the meeting.

Trump told the lawmakers that the House bill didn't go far enough in protecting individuals in the marketplace -- and appeared to use that as his rationale for why he has ambiguously called twice for the Senate to "add more money" to the bill.

The positive comments about the Senate plan tracks with Trump telling reporters during the meeting that the Senate should spend more on the bill to make it "generous, kind (and) with heart."

But the comment belies the celebratory Rose Garden ceremony Trump hosted earlier this year when the House passed the bill and the President championed it as "incredibly well crafted."

The luncheon, which brought together the eclectic group of Republican lawmakers, was organized to give the President a chance to check in on the process, not twist arms with the hope of striking a deal, a White House official said.

But his call for more funding could make it more difficult to sell the bill to House Republicans, who will meet with senators if the bill passes the Senate to reconcile the differences between the two legislative bodies.

Additionally, according to Senate rules, the bill passed through the body has to save $133 billion, the same amount of money as the House bill. That leaves Trump and Senate Republicans with little flexibility on spending. While they can spend more money on certain areas, they still have to hit the $133 billion marker to comply with Senate rules.

Republicans currently face a do-or-die moment to pass a bill. Since the House passed Obamacare repeal earlier this year, Senate Republicans have been crafting their own repeal bill behind closed doors. Now, facing a deadline if they want to finish the legislation this summer, the Trump administration is looking to step up pressure on GOP senators.

"He made pretty clear that he thinks the House bill leaves people -- many of which probably make up his base -- in a bad place," one congressional source with direct knowledge of the meeting said.

While the meeting didn't include an in-depth policy discussion, it did touch on how Senate Republicans are working to re-structure the tax credit in order to address lower income and older individuals.

"He's happy with our direction, and that direction is a departure from the House effort," another source, asked to summarize the meeting, told CNN.

Trump, according to senators who attended, urged quick action on health care, casting the debate as a promise Republicans made to voters that needs to be kept.

"The message was that we need to get this done, it needs to be done right, but sooner is better than later," said Sen. John Thune of South Dakota, adding that Republicans can't move to other aspects of their agenda before they pass reform.

Trump's lunch included a number of more moderate Republicans, including Sens. Rob Portman of Ohio, Lisa Murkowski of Alaska and Susan Collins of Maine, and conservatives like Sens. Joni Ernst of Iowa, Pat Toomey of Pennsylvania, Ted Cruz of Texas and Mike Lee of Utah.

Portman, Cruz, Lee and Toomey are all members of Senate Republicans' working group on health care. Vice President Mike Pence, who has worked with Senate Republicans for weeks on health care, also joined the lunch.

Portman told reporters the group also discussed how to get insurers back in the marketplace quickly. And Collins said Trump was "receptive" to "suggestions" about cost-sharing reduction payments that lower deductibles and co-payments.

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The Ohio Republican acknowledged the meeting didn't appear to resolve any differences, but added "that wasn't the purpose."

One GOP Senate aide said there wasn't a lot of substance in the meeting.

"I think the whole point of the meeting was just the television shot of Trump surrounded by Ernst and Murkowski," the aide said.

The lawmakers specifically discussed structuring the bill differently than the House bill, Thune said, including ensuring the bill "protects people with pre-existing conditions" and using tax credits to "make the bill work for lower income, elderly people."

"I think he realizes our bill is going to move probably from where the House was and he seems fine with that," Thune said. "But I think he wants us to be able to do our work and he feels good about the progress that we've made. But he wants to get the job done."

Referring to Obamacare as a "disaster," Trump told reporters who briefly attended the meeting that the legislation he hopes to sign would be "phenomenal for the people of our country."

"Generous, kind, with heart. That is what I am saying," Trump said. "And that may be adding additional money into it. We are going to come out with a real bill, not Obamacare."

Trump has so far largely left the Senate to do its work, remaining hands off through a difficult process. His legislative affairs team has been closely involved, but the President himself has been removed -- by design, multiple aides on Capitol Hill said.

The President will likely accept whatever they come up with -- "Pretty obviously (he's) not a details guy," one Republican aide said -- but will eventually be called on to help rally support for the final product.

Trump will also meet with "Obamacare victims" on Tuesday when he travels to Wisconsin. Trump met earlier this month with families adversely impacted by growing Obamacare premiums in Ohio.

House Republicans "have done (their) job," Trump said in Ohio, and "now it is the Senate's turn to act, and again, I hope they are going to act in a very positive manner."

"We're keeping our promise to the American people," Trump said Tuesday.

Time is of the essence. Senate Majority Leader Mitch McConnell is still targeting a vote before the July 4 recess, even if there are only 14 working days left.