Larry Kudlow, director of the U.S. National Economic Council, speaks during a news conference in the briefing room of the White House in Washington, D.C., on Friday, Jan. 17, 2020.

The stimulus package under negotiation in the Senate to combat the economic damage from the coronavirus pandemic will likely total more than $2 trillion, White House Economic Advisor Larry Kudlow said on Saturday.

The package is equal to about 10% of U.S. economic output, Kudlow told reporters as he went to a meeting with Republican senators on Capitol Hill. It's a major escalation at roughly twice the size of the package the administration requested only several days ago.

"We're just trying to cover the right bases," Kudlow said. He also said that small businesses would receive a payroll-tax holiday, though it's unclear whether that's been agreed upon or is an item on the agenda.

The Senate has been under immense pressure to finish a relief plan with the House and administration as quickly as possible. Lawmakers this weekend are pushing to meet the Trump administration's Monday deadline of coming to an agreement.

The proposed $2 trillion package is the third coronavirus relief package. President Trump this week signed a $100 billion aid package that includes provisions for emergency paid leave for workers and free testing. That came after he signed a $8.3 billion package earlier in the month to provide federal aid to government health officials and vaccine research and development.

Unemployment claims next week could total three million, Bank of America said this week, as some workers get laid off without severance, paid leave or health insurance. Hospitals are also facing equipment and staff shortages amid the crisis.

The Trump administration is under pressure over the shortage of important medical supplies. President Trump at a Saturday press briefing said he hasn't used the Defense Production Act, which would order private sector manufacturing of supplies like masks and ventilators, because the administration has seen some corporations volunteering help.

Asked about the potential $2 trillion price tag for the latest relief package, the president said: "I've spoken directly or indirectly to everybody many, many times...I think the Democrats and the Republicans are going to come up with a package that's going to be really something."

Across the U.S., millions of Americans are being told to isolate themselves as coronavirus cases in the country pass 19,000, killing at least 260 people so far. Forty-five states have shut down all schools, and bars and restaurants have also closed in many areas as governments ban group gatherings.

California and New York, among the largest economies in the U.S., have shut down all nonessential businesses indefinitely in an effort to contain the spread of the virus. Similar drastic measures have been taken or are planning to be taken in New Jersey, Illinois and Connecticut.