The path toward a bipartisan coronavirus aid package was hard to see Tuesday, as some Republicans declined to back their own new plan and Democrats leveled fresh attacks against it.

One day after Senate leaders unveiled a roughly $1 trillion plan for pandemic relief, Republicans struggled to offer a united front on a measure that some consider too costly. Sen. Lindsey Graham, R-S.C., said “close to half” of the GOP caucus could end up opposing a package of that size.

“I have problems with a number of provisions,” said Sen. Patrick J. Toomey, R-Pa. “I’ll wait and see what the final product looks like, but I’m pretty skeptical about the way it seems to be shaping up.”

The divided caucus could strengthen the hands of Democrats as bipartisan talks get underway on a compromise package.

Acknowledging that risk for his party, Sen. John Cornyn, R-Texas, urged Republicans not to “take themselves out of contention” by refusing to consider the relief package now before them. “If it’s passed with mainly Democratic votes, obviously they’re going to have a disproportionate influence on what’s in it,” he said.

But Senate Majority Leader Mitch McConnell said Democrats would have to give ground on the nearly $3.5 trillion plan the House passed in May. Refusing to accept Republican initiatives, he said, could result in nothing getting passed, like when Democrats blocked a GOP bill aimed at reducing police brutality in June.

“Democrats face a simple choice,” McConnell said on the Senate floor. “They can come to the table, work with Republicans and engage seriously to make law for the American people. Or they can stay on the sidelines, point fingers and let another rescue package go the same way as the police reform bill they killed in June.”

A second consecutive day of talks between Democratic leaders and White House officials produced another round of recriminations. “It seems to me that Sen. McConnell doesn’t want to get an agreement made,” said Speaker Nancy Pelosi, referring to the majority leader’s insistence on liability protection for employers during the pandemic. “It wasn’t a good way of us to start the discussion this afternoon.”

And top White House officials did little to hide the frosty tone of their meeting. “We still obviously have a lot of work to do,” said Treasury Secretary Steven Mnuchin.

“I don’t know that I would characterize it as getting closer” to a deal, added White House Chief of Staff Mark Meadows. He said Democrats haven’t given any ground on their push to extend the $600 added weekly unemployment benefit that expired this week, for instance. Republicans want to pare that to $200 through September, until states can work out a plan to replace 70 percent of lost wages.

Republicans are trying to reach a bipartisan deal even as they struggle to overcome divisions within their own ranks. But Cornyn, the Senate’s former No. 2 Republican, said he thought most GOP senators were still open to supporting the measure.

“I haven’t heard anybody that’s completely locked down as a ‘no’ vote yet,” Cornyn said. “I would view this more as sending a few warning shots.”

But if Republicans were firing “warning shots,” Democrats were throwing grenades. Senate Minority Leader Charles E. Schumer trashed the proposal on the floor, saying it is “littered with corporate giveaways, K Street handouts and presidential pet projects.”

The New York Democrat singled out for criticism the inclusion of $1.75 billion for a new FBI headquarters sought by the White House to replace the current headquarters that sits on Pennsylvania Avenue across from the Trump International Hotel. Democrats have pushed for a new headquarters in the Maryland or Virginia suburbs, saying the FBI needs a more secure, campus-like location.

“Senate Republicans managed to sneak in nearly $2 billion in taxpayer funds for a new FBI building whose location will increase the value of the Trump Hotel and enrich the president and his family,” Schumer said.

McConnell acknowledged the divisions within his own party over a package whose release had been delayed last week to allow for intensive negotiations with the Trump administration.

“It’s a statement of the obvious that I have members who are all over the lot on this,” McConnell said at his weekly news conference. “We’ve done the best we can to develop a consensus among the broadest number of Republican senators, and that’s just the starting place.”

The GOP package, dispersed among eight separate bills, would offer a new round of tax rebate checks to families, a slimmed-down version of extended unemployment benefits, $306 billion for federal agencies to respond to the pandemic, a new round of Paycheck Protection Program small-business loans, expanded payroll tax credits to encourage hiring and retention, and more.

But the package amounts to less than a third of the size of a competing House Democratic measure and falls far short of what Democrats are seeking. Among the biggest sticking points to resolve are the size of extended unemployment benefits, whether to provide employers with liability protection from pandemic-related medical claims, and whether to come to the aid of state and local governments that face the risk of layoffs and furloughs.

Signs of flexibility

Even so, there were signs that lawmakers would leave themselves room for compromise.

Sen. Roy Blunt, R-Mo., a senior appropriator, said he was open to providing money to help states secure their elections this fall during the pandemic — although he would not back the full $3.6 billion that House Democrats are seeking. “I’m certainly in favor of adding some money, assuming the case can be made for some more reasonable number than $3.6 billion, which is a totally indefensible number,” he said.

Senate Banking Chairman Michael D. Crapo, R-Idaho, said he was hopeful that a compromise package would extend a moratorium on evictions for renters, even though it’s not part of the GOP measure. “There will be something, I hope, dealing with rental assistance,” he said.

Benjamin L. Cardin of Maryland, the top Democrat on the Senate Small Business Committee, said the two parties “are pretty close” on finding a compromise for an extended Paycheck Protection Program.

There’s no direct aid in the Senate bill for state and local governments, although Republicans say about $105 billion for education would help alleviate their burdens. House Democrats included $915 billion in their bill, but Meadows said Pelosi and Schumer didn’t call that figure a “red line” in their meeting.

In another sign of flexibility, McConnell distanced himself from the money for a new FBI headquarters in downtown Washington. He said he favors removing all “nongermane” items from any final package, including FBI funding, which he made clear was sought by the White House.

Piecemeal approach

Still, it wasn’t clear that a compromise could be struck and passed by the end of next week, before the scheduled August recess. “I’m opposed to passing something right now,” said Senate Homeland Security and Governmental Affairs Chairman Ron Johnson, R-Wis., who held a hearing Tuesday on how pandemic relief money has been spent.

Republicans also appeared divided on whether to pass a relief package in piecemeal fashion, possibly starting with an extension of expanded unemployment benefits that expire this week. White House officials have been pushing for a piecemeal approach.

“The important thing is that we end up with a good package that we can support that addresses the need. And if we need to do it in a couple of steps, that’s OK,” said Sen. John Hoeven, R-N.D.

But Cornyn threw cold water on that idea Tuesday. “I don’t hear any support for that,” he said. “I mean, I’ve heard people float it, but I haven’t heard any support for that.”

Lindsey McPherson and Jennifer Shutt contributed to this report.