Senate Budget Committee Chairman Kent Conrad (D-N.D.) announced Wednesday that Democrats had finally reached an agreement on a budget plan.

His announcement came as the leadership met with President Obama to inform him that their members had unified around a message for the debt-limit showdown.

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Conrad’s proposal, which he said he plans to introduce as soon as next week, would cut more than $4 trillion from the deficit, a greater reduction than what Obama’s fiscal commission had recommended.

“We’ve reached an agreement after weeks of work,” Conrad told The Hill on Wednesday afternoon. “I think it’s big.”

Democrats have also settled upon the message they want Obama to push in the public battle with Republicans over the $14.3 trillion debt limit, which Treasury says must be raised by Aug. 2.

The fundamental message to the president is that any deficit-reduction deal with Republicans must be based on the principle of “fairness.”

The deal cannot cut Medicare benefits or slash Medicaid. It must raise tax revenues. It should make investments in infrastructure and green-energy technology to spur job growth. It should cut defense as well as domestic social spending.

“The message is we know what our priorities are; we’ve said them over and over again; let’s make sure we’re on the same page with those priorities. Our understanding is Social Security, Medicare, Medicaid and the middle class will be protected and everyone will pay a fair share,” Sen. Barbara Boxer Barbara Levy BoxerThe Hill's Morning Report - Presented by Facebook - Biden, Harris launch Trump offensive in first joint appearance Bottom line Polls show big bounce to Biden ahead of Super Tuesday MORE (Calif.), a senior member of the Democratic Conference, said of the message leaders would take to the president Wednesday.

Sen. Jay Rockefeller John (Jay) Davison RockefellerBottom Line World Health Day: It's time to fight preventable disease Lobbying World MORE (D), whose constituents in West Virginia depend heavily on federal support for Medicaid, said he has insisted that Senate Majority Leader Harry Reid Harry Mason ReidGOP senators confident Trump pick to be confirmed by November Durbin: Democrats can 'slow' Supreme Court confirmation 'perhaps a matter of hours, maybe days at most' Supreme Court fight pushes Senate toward brink MORE (D-Nev.) remind Obama to protect the program.

“The caucus wants to see revenues on the table, they want to see cuts in the Defense Department, they want fairness,” Rockefeller said.

Democratic leaders have ruled out cuts to Medicare benefits. Rockefeller said he has helped convince them to take Medicaid cuts off the table as well.

“I worked very hard for that in a meeting,” he said. “I just kept at it.

“I think if Republicans put revenues on the table, then my fear is the administration will say, ‘OK, now let’s go get Medicaid,’ because it’s the third-largest program in government,” he said.

Rockefeller could accept some cuts to Medicaid, but not a massive across-the-board cut.

“We all need to be steeled,” he said. “Democrats aren’t very good at messaging.”

Wednesday’s meeting at the White House included Reid, Democratic Whip Dick Durbin Richard (Dick) Joseph DurbinSupreme Court nominee gives no clues in GOP meeting Warren won't meet with Barrett, calling Trump's nomination an 'illegitimate power grab' Conservative group unveils ad accusing liberals of attacking Barrett's faith MORE (Ill.), Democratic Policy Committee Chairman Charles Schumer Chuck SchumerDemocrats rip Trump for not condemning white supremacists, Proud Boys at debate Warren won't meet with Barrett, calling Trump's nomination an 'illegitimate power grab' Schumer won't meet with Trump's Supreme Court pick MORE (N.Y.) and Democratic Senatorial Campaign Committee Chairwoman Patty Murray Patricia (Patty) Lynn MurrayPoll finds support for independent arbiters resolving 'surprise' medical bills Senate Democrats introduce legislation to probe politicization of pandemic response Trump health officials grilled over reports of politics in COVID-19 response MORE (Wash.).

Some Democrats are leery of Obama giving up too much ground to Republicans in a major deficit-reduction deal.

They carry uncomfortable memories of the agreement Obama forged with Senate Republican Leader Mitch McConnell Addison (Mitch) Mitchell McConnellIn rare move, Schumer forces vote to consider health care bill amid Supreme Court tensions COVID-19 talks hit crucial stretch Supreme Court nominee gives no clues in GOP meeting MORE (Ky.) in December, which extended almost all of the Bush-era tax cuts. In return, the president won a yearlong extension of unemployment benefits.

As months pass and Republicans push for trillions in spending cuts while refusing to consider any tax increases, that December deal has begun to look to many Democrats like a missed opportunity.

Democrats have become exasperated at Republican leaders’ staunch refusal to even consider ending special tax breaks to reduce the deficit.

Republicans are threatening to block the debt-limit increase unless Democrats agree to massive spending cuts, and have insisted on cuts to Medicare.

Economists including Federal Reserve Chairman Ben Bernanke have warned that failure to increase national borrowing authority could crash the economy, but those warnings have done little to shape public opinion. Polling still shows more Americans oppose raising the debt limit than support doing so.

Some Democrats complain the president needs to use his bully pulpit more aggressively to pressure Republicans to agree to a debt-ceiling increase.

Obama responded to the criticism Wednesday by making a forceful presentation at one of his first news conferences in months. He took direct aim at Congress and challenged lawmakers to skip their recesses until deficit negotiations are solved.

“They’re in one week. They’re out one week. And then they’re saying, ‘Obama’s got to step in,’ ” the president said. “You need to be here. I’ve been here. I’ve been doing Afghanistan and bin Laden and the Greek crisis and — you stay here. Let’s get it done.”

Obama criticized Republicans for defending special tax breaks for corporate jets and major oil companies, something Democratic lawmakers had been waiting for weeks for him to do.

Buzz about the speech quickly spread around the Senate floor as lawmakers voted Wednesday.

Senate Democratic leaders discussed the possibility of canceling the Senate’s July 4 recess and convened a special meeting with rank-and-file members Wednesday afternoon to discuss next steps.

The collapse of the deficit-reduction talks led by Vice President Biden has instilled a new sense of urgency and unity among Democratic lawmakers. They say Republicans are prepared to take the standoff to the brink of a national default and must coalesce to put up effective opposition.

“Right now we’re marshaling our forces,” said Sen. Ben Cardin Benjamin (Ben) Louis CardinPelosi hopeful COVID-19 relief talks resume 'soon' Congress must finish work on popular conservation bill before time runs out PPP application window closes after coronavirus talks deadlock MORE (D-Md.). “Clearly the bipartisan negotiations have not produced. There is a real concern about whether we’ll have a real plan to reduce the deficit, which is something that was our objective.”

The emergence of a Senate Democratic budget deal as soon as next week will give them ammunition in the public battle they expect over the final weeks of the debt-limit debate.

“Let’s be very clear on our priorities. It starts, No. 1, with a credible plan to deal with the deficit. No. 2, it’s fairness, it has to include all the elements. No. 3, we need to protect our most vulnerable and our economic job growth,” Cardin said. “There are the principles. Let us now show the American public what type of deficit plan would accomplish those three objectives.

“Starting there, let’s get as far as we can,” Cardin said.