Congressional Republicans have strongly backed President Trump’s efforts to respond to the deadly coronavirus pandemic and its crippling impact on the economy, even as many of their home state officials have pushed for more to be done.

But on the issue of testing, some Senate Republicans are looking for ways to get the federal government to play a bigger role despite Trump’s insistence it is an issue that governors should handle.

Led by Sens. Lamar Alexander (R-Tenn.) and Roy Blunt (R-Mo.), Senate Republicans have largely envisioned the federal government taking a lead role in experimenting with diagnostic and serological tests for the coronavirus, even if some of the ideas ultimately fail — the thinking being that the government can take chances that perhaps the private sector cannot.

“We’re encouraging some risk-taking here,” Blunt said in an interview Tuesday. There is about $1 billion allocated for that effort in the a $484 billion economic stimulus agreement that cleared the Senate on Tuesday afternoon.

Sen. Bill Cassidy (R-La.), has proposed a centralized immunity registry that would track who would be protected from infecting others with the coronavirus, modeling it on existing systems for other diseases that record who has been vaccinated. The new agreement gives the Centers for Disease Control and Prevention $1 billion to be used in part for surveillance to determine who is infected.

“If we are going to be able to figure out how to open up the economy again, and prior to having at least a vaccine, then we’ve got to figure out who has the virus and who doesn’t,” said Senate Majority Whip John Thune (R-S.D.).

Senate Republicans remain united in agreement with the president that the administration of coronavirus tests should be left to state and local public health agencies.

“I really believe . . . the more local something is, they probably can do a better job,” said Sen. Rick Scott (R-Fla.), who ran a private for-profit health-care company before his time in public office. “The feds can fund things, but not run things well.”

The dispute over how to efficiently run testing was one of the remaining hurdles resolved in a $484 billion economic stimulus agreement finalized Tuesday, which would also replenish a new small-business lending program whose funds ran dry last week. In addition to more money for testing, Democrats insisted on a new reporting regimen that Senate Minority Leader Charles E. Schumer (D-N.Y.) touted as a key win.

During the negotiations, the White House — which wanted to delegate more responsibility to the states — and Republican negotiators were concerned Democrats were trying to craft a reporting system that would more easily pin the blame on the Trump administration for any shortfalls, according to GOP senators and aides who spoke on the condition of anonymity to describe the private talks.

The agreement includes $25 billion for tests, including a national strategic testing policy highlighted by Democrats that Republicans said will still leave enough flexibility to state and local health departments, including more money to increase their capacities to administer them.

Thune said the agreement Tuesday strikes a balance — giving states more resources to carry out the tests, but “it also recognizes that the federal government has a role.”

Democrats had called for a $30 billion testing plan that would create a comprehensive national testing strategy and put the onus on the administration to allocate tests and create a pipeline to ensure there are enough of them nationwide.

“There’s a reason that people that run the executive branch are called the administration,” because they administer, said Sen. Angus King (I-Maine), who caucuses with Democrats and said he was infuriated after a call with Democratic senators and Vice President Pence last week over what Democrats said were inadequate answers about a national testing strategy.

The clashes over testing have been most acute between governors and Trump when it comes to the shortfall of tests and supplies — particularly with Trump’s decision to let states largely fend for themselves and his reluctance to fully invoke the powers of the Defense Production Act.

In a Washington Post Live interview Tuesday, Illinois Gov. J.B. Pritzker (D) said states still need Trump to enact the obscure law so local health departments can more readily obtain testing supplies such as cotton swabs and reagents.

“None of that has been done at the federal government level. That’s the mistake that has been made all along here,” Pritzker said. “We could have organized this and led this at a federal level.”

While Trump’s plans to use the Defense Production Act to boost the development of testing swabs have been beset by mixed messaging and contradictory claims, officials said the effort was moving ahead.

Trump initially said he was planning to invoke the act because he’s “had a little difficulty” with one swab manufacturer, but senior administration officials contradicted him by saying the White House was instead cooperating with Maine-based Puritan Medical Products to produce more swabs.

Under the law, the government will incentivize, rather than force, Puritan to step up swap production.

“This is the hand up. This is the government coming in and saying, ‘How can we help you expand your lines?’ ” Brett Giroir, the federal official overseeing coronavirus testing efforts, told reporters Monday. “There’s no asynchrony here at all.”

Brad Smith, director of the Center for Medicare and Medicaid Innovation, told reporters Monday that efforts to use the Defense Production Act were underway, with Puritan actively negotiating with the Pentagon over how to build four new production lines and begin making 20 million additional swabs monthly.

But Trump added to the confusion minutes later about the act, saying that “we really don’t need it,” making the case that the threat of invoking the powerful war-era legislation had been enough. The White House press office did not respond to requests for clarification.

Trump and New York Gov. Andrew M. Cuomo (D) met in the Oval Office on Tuesday to discuss testing, with the president telling reporters that the two leaders spoke to discuss Cuomo’s statewide testing strategy and “how we can work together to help expand it, with the goal of doubling testing in the next few weeks.”

Former vice president Joe Biden, the presumptive Democratic presidential nominee, has aggressively criticized Trump over testing, arguing the president has failed to use his powers appropriately.

“Instead of quickly and fully deploying the Defense Production Act to secure materials like swabs to ramp up our testing capacity — as I called for over a month ago — Trump is only now beginning to address the shortage of swabs after an unacceptable test slowdown that has left us far below where we need to be to reopen our country, and with countless Americans left with horrible uncertainty as they and their loved ones fight this disease,” he said.

Meanwhile, as partisan tensions flare, some governors have gotten creative in getting what they need.

Louisiana Gov. John Bel Edwards (D) told reporters last week that his state had been using 3-D printers to develop testing swabs, but continued to face a shortfall of reagents. Widespread testing, he said, would be key to reopening Louisiana’s economy.

Edwards said the state had ramped up testing significantly in recent weeks, but it still “was not as robust as we would like.”

And Maryland Gov. Larry Hogan (R) enlisted his wife, Yumi Hogan, to negotiate with her home country of South Korea to secure 500,000 coronavirus tests, which arrived Saturday at Baltimore-Washington International Marshall Airport and will help to dramatically expand Maryland’s ability to quickly identify patients sickened from the virus.

Trump didn’t appear too pleased with the Hogans’ efforts to go abroad, saying Monday of the Maryland governor, “I think he needed to get a little knowledge, would’ve been helpful.”