By Kevin Liptak, CNN

(CNN) -- Hours before President Joe Biden was set to meet with a group of Republican senators proposing a drastically slimmer coronavirus relief package than the $1.9 trillion measure he is offering, the White House said the session would not be used to negotiate a new number.

"This meeting is not is a forum for the President to make or accept an offer," press secretary Jen Psaki told reporters during a midday briefing, defending the administration's figure as necessary to address the dual health and economic crises facing the nation nearly a year into the deadly pandemic.

The message appeared to signal to Democrats and Republicans alike that despite Biden's professed desire to achieve bipartisan consensus on a relief bill, he remains intent on pressing for his own proposal even as he hears out the views of Republicans.

The 5 p.m. ET meeting with the 10 GOP senators, led by moderate Republican Sen. Susan Collins of Maine, is Biden's first publicly disclosed Oval Office session with lawmakers since taking office last month. That it is occurring with Republicans and not Democrats advances the notion he is intent on at least appearing to foster "unity," the motto of his administration.

Psaki said Monday the session is an example of Biden's commitment to a bipartisan exchange of ideas.

"He felt it was, you know, an effort to engage and engage on a bipartisan basis, and that's why he invited them to the White House today," Psaki said. She sought to emphasize Republican support for a large relief bill by citing interviews West Virginia Gov. Jim Justice gave earlier in the day, including on CNN, when he urged against holding back.

"If we actually throw away some money right now, so what?" the Republican governor said on "Newsroom."

Psaki said Biden will engage with Democrats in the Oval Office in the future, and emphasized the need to move ahead. He spoke with the two top congressional Democrats, Senate Majority Leader Chuck Schumer and House Speaker Nancy Pelosi, on Sunday.

"It's incredibly urgent," Psaki said, citing access to unemployment insurance, food insecurity, and the need for funding for vaccine distributions and public schools.

At the same time, she downplayed the prospects of Biden approving of the Republicans' bill, which at $618 billion comes in at less than half of Biden's plan.

"There is obviously a big gap between $600 billion and $1.9 trillion. I don't believe any of us are mathematicians, but clearly the amount needs to be closer to what he proposed than smaller," Psaki said during Monday's press briefing.

Asked if it was more important for the bill to be big or bipartisan, Psaki said Biden believes he can have both.

"Well, I think the President believes we can, and there is a historic evidence that it is possible to take a number of paths, including through reconciliation, if that is the path that's pursued, and for the vote to be bipartisan," Psaki said. "But it's important to him that he hears this group out on their concerns, on their ideas."

The administration is facing a crucial test this week. In addition to the President's meeting, Democrats are beginning the reconciliation process to potentially pass legislation on their own, which could potentially poison the well for a bipartisan deal.

Many Democrats in Congress believe entertaining Republican counteroffers is merely putting off the inevitable, and would like Biden to proceed quickly to using reconciliation to pass a bill with only a 51-vote majority.

But though he insisted on Friday that Covid relief must pass soon -- "no ifs, ands or buts" -- Biden remains hopeful of fostering Republican support.

On Sunday, the White House said Biden had spoken to Collins and invited her, along with nine other Republicans, to the White House.

The other invited participants in the meeting are GOP Sens. Bill Cassidy of Louisiana, Shelley Moore Capito of West Virginia, Todd Young of Indiana, Jerry Moran of Kansas, Mike Rounds of South Dakota and Thom Tillis of North Carolina.

The Republicans' plan places more emphasis on the health effects of the crisis, including by expanding funds for a vaccine rollout. It limits direct payments to Americans and does not include assistance to states and localities, which Democrats have insisted upon as part of any relief measure.

The White House is hoping to move quickly, both to stave off further economic pain and to launch his administration with a legislative win. Certain unemployment benefits also expire soon, lending urgency to the talks.