Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSchumer: Fauci may testify before Senate next weekThe next big battle on Capitol Hill concerns aid to states and localitiesGOP senator lifts two-year hold on Trump’s nominee for counterintelligence chiefMORE (R-Ky.) is coming under pressure to increase testing for the coronavirus in the Senate amid concerns that the Capitol could become a hot spot and wind up spreading infection around the country.

Senate Health Committee Chairman Lamar AlexanderAndrew (Lamar) Lamar AlexanderNIH launches ‘Shark Tank’-style contest to develop new testing technologiesRepublicans sharply divided over timeline for reopening economyUnion leader asks Pelosi, Schumer to spike ‘surprise’ billing legislationMORE (R-Tenn.), one of McConnells close allies who is retiring at the end of this Congress, pressed the GOP leader on Tuesday to have all members of the upper chamber tested for the highly contagious virus before flying back to their home states.

Members of Congress would represent sort of a virus-spreading machine, coming in here to a coronavirus hot spot and then going home, Alexander told reporters after attending a lunch meeting of Republican senators Tuesday.

Alexander, who has taken the lead for GOP senators on assessing the deployment of tests, said McConnell knows my thoughts.

It doesnt make a lot of sense to fly 535 people in from all over the country to a coronavirus hot spot and then send them home on Thursday and Friday. It would take an army of public health workers to track and trace all the people they might have exposed, he said.

Congresss attending physician, Brian Monahan, notified GOP leaders last week that only senators who show signs of sickness would be tested for the coronavirus and that it would take two days to get results.

That prompted the Trump administration on Friday to offer sending three Abbott point-of-care testing machines to Capitol Hill along with 1,000 tests.

In a rare bipartisan statement, McConnell and Speaker Nancy PelosiNancy PelosiThe next big battle on Capitol Hill concerns aid to states and localitiesPelosi slams White House for blocking coronavirus task force members from testifying: ‘They might be afraid of the truth’Parties divided over health risks to reopening CapitolMORE (D-Calif.) declined the rapid-testing machines, urging the administration in a joint statement to send them to the front-line facilities where they can do the most good the most quickly.

Alexander, 79, on Tuesday said leaders should reconsider to avoid the risk that Congress itself becomes an engine for spreading infection.

I think there will be a very rapid change in attitudes about accepting the presidents offer to test members of Congress for COVID-19, especially as the House comes back, he said.

Were doubling the amount of testing up to 2 million a week, there ought to be enough tests to test 535 members of Congress who come to one of the nations coronavirus hot spots before they go back home around the country and infect people in their districts, he added.

Alexander made his pitch for more testing of members of Congress during a Senate Republican luncheon Tuesday.

A Republican senator who attended a Tuesday lunch meeting later told reporters he agreed with Alexander.

As we get more testing it will be easier to do it than this week. So probably next week it will be easier, and its got to be a fast and accurate test, said the lawmaker, who requested anonymity to discuss Alexanders comments. The senator predicted that many colleagues would fly back to their home states this week.

House Minority Leader Kevin McCarthyKevin Owen McCarthyParties divided over health risks to reopening CapitolHouse Democrat calls for halt to lawmakers sleeping in their officesGOP leader disagrees with Pelosi, McConnell on WH testing offerMORE (R-Calif.) told Politico Monday that he disagreed with McConnell and Pelosis decision to forgo rapid-testing kits from the White House.

I do believe it would be critical to have the testing here because there will be a flare-up, he said.

Trump criticized the move, tweeting: No reason to turn it down, except politics. We have plenty of testing. Maybe you need a new Doctor over there. Crazy Nancy will use it as an excuse not to show up to work! 

Other Republican senators are raising concerns about flying back and forth to states around the nation in the middle of a pandemic when the Centers for Disease Control and Prevention has warned travel increases your chances of getting and spreading Covid-19.

Flying from a hot spot such as Washington, D.C., which has a stay-at-home order in effect until at least May 15 and has more than 5,000 reported coronavirus cases, to states with lower incidences of infection could spread the disease.

I find it concerning that we as members would come from all parts of the country to gather here for a few days during the workweek and then dissipate around the rest of the country to our home states only to come back on Monday. That to me is concerning, said Sen. Lisa MurkowskiLisa Ann MurkowskiMcConnell rejects calls to cancel Senate schedule amid pandemicTrump floats funding for oil after historic market lossOvernight Energy: EPA weakens power plant pollution rule | DOJ lets companies skip paying penalties during pandemic | Trump eyes plan to pay companies to keep crude in the groundMORE (R-Alaska), whose home state is more than 3,000 miles away from the nations capital.

Thats how our schedule worked pre-COVID. We are in COVID, and I think we need to adjust our schedules accordingly. I know some didnt particularly want to come back. I didnt leave. I havent been home since March 8, she said.

What I am concerned about is that we would engage in a level of travel we have told Americans that you should not be traveling unless its absolutely necessary, she added.

Murkowski said she agreed with Alexanders call for more testing but also had respect for McConnells decision to send rapid-testing kits to front line health workers.

I think we all need more testing. Sen. Alexander was eloquent as always when he said in order to get back to work and get back to school we need testing and he is absolutely right, she said. I want to support every initiative that will get us on that track because its not only important for us in the Senate, its important for the fisheries that we want to start happening in Alaska in two weeks. Its important for our oil-field workers to get back to work.

Its important for everybody to have that level of testing, she added.  

Murkowski also said she understood McConnells calculus for passing on the White House offer of rapid-testing kits.

Should we be given access to something that the American public as a general rule doesnt have access to? No, she said. So I respect the decision that was made.

Many Senate Republicans attended their weekly conference lunch meeting in the Hart Senate Office Building in person Tuesday and plan to be physically present at future lunches.

Senate Democrats, by contrast, plan to meet by conference call instead of attending regular lunch meetings as they did when the pandemic hit.

And while Republicans showed up in person for hearings in person on Tuesday, Democrats attended the sessions via a video-conferencing linkup.

Senate Democratic Whip Dick DurbinRichard (Dick) Joseph DurbinSome Democrats say charges against Biden merit independent investigationBipartisan Senate bill would make more green cards available to doctors, nursesSenate Democrats call on administration to provide COVID-19 testing for migrants before deportationMORE (Ill.) said he was undecided about showing up at the Capitol this week.

I dont think we should have come back, he told reporters Monday, arguing that Republicans should be working on coronavirus relief legislation instead of advancing Trumps judicial nominees.  

I contemplated not coming, I contemplated driving, Durbin confessed. But he said he decided to fly to Washington, D.C., after conferring with the attending physician.

On Tuesday, Durbin, 75, told reporters that every interaction in the Capitol carries a health risk.  

Being here today your being here today is a risk to both of us and to our families. Its just a fact, he said. Its a risky decision.