(CNN) — Republican leaders in both chambers are maneuvering to keep all of their members in line against the $1.9 trillion Covid-19 relief plan, a move that would deny President Joe Biden a bipartisan victory and one that could scuttle the bill in the Senate if any Democrat breaks ranks.

But the move amounts to a political risk for Republicans with polls showing clear majorities of Americans supporting an emergency rescue package and with the economy still reeling from the coronavirus pandemic.

So Republicans now plan to begin an urgent public relations push to argue that the bill is bloated, poorly targeted and contains a hodgepodge of measures aimed at pleasing the Democratic base — a message that party leaders discussed with their members at a private GOP lunch on Tuesday and that they plan to echo in the days ahead, attendees say. And Republicans hope that after months of bitter party infighting, they can now finally unite and take their battle toward Democrats — and not each other.

“If the Democrats continue down the path they’re on, and that is to not make any attempt to try and get Republican input or ideas, it makes it hard for any of our members, even those that might be inclined to do so to vote for it, to vote for anything,” said Senate Minority Whip John Thune told CNN. “So, if it’s in its current contours, it’s hard to see very many, if any, Republicans being for it, especially given the way the Democrats have approached it.”

At the lunch on Tuesday, GOP senators talked at length about the Democrats’ bill, with attendees criticizing it in sharp terms. They discussed their strategy for putting Democrats in a difficult political spot when amendment votes happen next week in the Senate, while also putting forward some middle-of-the-road amendments that could attract some Democratic support, according to attendees.

And afterward, Senate Minority Leader Mitch McConnell blasted the Democrats’ plan as “totally partisan,” while acknowledging that his party had work to do on its messaging in the face of public support for the Biden plan.

“I’m sure everybody would love to get a check,” McConnell said, referring to the checks of up to $1,400 for certain individuals in the proposal. “But they haven’t yet learned about what else is in it and part of our job as the substantial minority, remember we’re in a 50-50 Senate here, is to make sure the American people fully understand what’s being proposed.’

Democrats, however, argue that they have a mandate after winning the White House and the Senate and are taking urgently needed action to deliver aid to an American public suffering under the devastating toll of the ongoing pandemic. They have insisted they are willing to work with Republicans but will not water down the plan — a lesson they say they learned from then-President Barack Obama’s first stimulus plan in 2009.

“Democrats remain committed to working with our colleagues from the other side of the aisle … to improve the bill,” Senate Majority Leader Chuck Schumer said Tuesday. “But at the end of the day, the American people sent us here with a job to do, and the clock is ticking. Democrats will not wait to move forward with the American rescue plan.”

The bill — which includes a federal minimum wage hike to $15 per hour, staggering sums for schools, states and cities, along with an extension of jobless benefits and money for vaccine distribution and nutrition assistance — heads to the House floor by week’s end where Speaker Nancy Pelosi has little margin for error since Republicans are expected to unify against it. The House is going to vote on the bill Friday, House Majority Leader Steny Hoyer said on Twitter.

Hoyer told CNN on Tuesday night, “I don’t anticipate that,” when asked if he expected to lose any Democratic support in his chamber.

And while House GOP leaders are confident their members will fall in line, some are still mum about their plans.

“I haven’t decided yet,” Rep. John Katko, a New York Republican, said when asked if he would vote for the $1.9 trillion bill.

GOP leaders believe that the moment is similar to 2009, when a new Democratic President pushed through a major relief plan with scant GOP backing — more than a year before their party took back control of Congress, a message that former Vice President Mike Pence privately delivered to a group of conservative lawmakers on Tuesday afternoon.

Indeed, Republicans believe that public opinion will shift on the matter — eventually.

Asked if it will hurt Republicans to oppose a politically popular bill, Thune said: “Once we get the message out there about what it includes, how much it is, what the potential impacts are on the economy, minimum wage being a good example then I think we’ll see more. I think that’ll change.”

Thune added that the GOP will focus on how the money in the proposal would be spent on schools. “I think the school reopening issue is a really hot issue – particularly in suburbia,” he said.

If the House passes the bill, which is expected, it then heads to the Senate next week where the rules will prevent Republicans from employing a filibuster to block it, since Democrats are using a fast-track budget process known as reconciliation to advance the plan by just 51 votes. Yet Schumer has no margin for error in the 50-50 Senate, since any single Democratic defection could bring down the centerpiece of the Biden agenda — and at least two moderate Democratic senators have voiced concerns about the wage hike in the plan.

So far, the potential GOP swing votes have lambasted Democrats to argue they’ve been shut out of the talks — and have shown no willingness to vote for the proposal.

“There has been very little effort on the part of the White House to meet with us and to see if we can find a middle ground, a common ground of some kind,” Sen. Mitt Romney, a Utah Republican, said on Tuesday. “I think the leadership in the House and the Senate just wants to blast ahead with reconciliation without any input from Republicans at all, and that’s not the way good legislation is crafted. Good legislation has both sides working on things, knocking off the edges, finding a better and better bill.”

Indeed, several GOP swing votes, such as Sens. Susan Collins of Maine and Romney, have been irked at the White House’s handling of the proposal — and are signaling they are all but certain to vote against the plan. And in the House, Republican leaders are whipping their colleagues to fall in line — with GOP sources predicting that they won’t lose any votes on the floor when the bill is considered by the full chamber at the end of the week.

Collins said on Tuesday the Biden administration won’t budge from its topline price tag for the package. “I would be surprised if there were support in the Republican caucus if the bill comes out at 1.9 trillion even if we’re able to make some beneficial changes.”

And Collins faulted both Schumer and White House chief of staff Ron Klain, whom she signaled out after a group of 10 GOP senators met with Biden on the matter earlier this month.

“The problem is that the what appears to be productive talks, seem to be countermanded by the Democratic leader in the Senate,” Collins said. After praising Biden for being “very attentive” and “gracious” at their recent meeting, Collins said: “Ron was shaking his head in the back of the room the whole time, which is not exactly an encouraging sign. I thought that was unfortunate.”

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