Editor's Note: President Trump on Wednesday night signed a coronavirus relief bill that paves the way for Americans to access free testing and financial support during the pandemic. Read the latest updates here. Our original story appears below.

Washington — The Senate on Wednesday approved a coronavirus relief bill passed by the House last week that provides free testing and paid leave for certain workers as the White House solidifies plans for an even larger package to address the fallout of the pandemic.

The Families First Coronavirus Response Act, which was endorsed by President Trump last week, passed the Senate with a bipartisan vote of 90 to 8.

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Senate Majority Leader Mitch McConnell urged his fellow Republicans to pass the bill, known as "phase two," calling the package "a well-intentioned bipartisan product."

"I will vote to pass their bill," he continued. "This is a time for urgent bipartisan action, and in this case I do not think we should let perfection be the enemy of something that will help even a subset of American workers."

Meanwhile, the Treasury Department outlined the administration's proposal for the third phase of the response. In a memo, the administration asks for two rounds of direct cash payments to taxpayers, worth $250 billion each. The first payment would be made April 6, and the second would come on May 18.

The administration's request also includes $300 billion in small business loans, $50 billion for the airline industry and $150 billion for other "severely distressed" industries. The document outlining the request was first reported by The Washington Post, and a senior administration official confirmed its authenticity to CBS News.

Some Senate Democrats complained that Republicans were not consulting them about this "phase three" bill.

"No one is talking to us at all," Senator Patty Murray said.

A senior White House official and a Senate GOP aide both noted that the proposal is the administration's wishlist, and is meant to be a jumping off point for the Republicans who are working on crafting the bill. There will likely be some variation on the final Republican Senate proposal. Once they have finalized their version, they will still have to work it out with Democrats in the House.

The House passed the phase two bill shortly after midnight on Saturday following lengthy negotiations between Speaker Nancy Pelosi and Treasury Secretary Steven Mnuchin. The bill passed on a bipartisan vote of 363-40 with Mr. Trump's endorsement.

The phase two package includes free coronavirus testing, expanded funding for food security programs, increased funding for Medicaid and state unemployment insurance, and paid sick, family and medical leave for workers at companies with 500 employees or fewer. The majority of workers in the country work at companies with more than 500 employees, many of which already offer paid leave.

The Senate considered amendments before moving forward with a vote Wednesday afternoon. Republican Senator Rand Paul introduced a failed amendment that would have required any additional spending to be offset by cuts elsewhere. Senator Ron Johnson, also a Republican, offered an amendment to the House bill which would remove the paid leave mandate while expanding eligibility for unemployment insurance for workers who lose their jobs during the crisis. Johnson's amendment did not receive the necessary votes to be added to the bill.

McConnell said Tuesday that senators will remain in Washington until they approve a phase three deal. "We're not leaving town until we have constructed and passed another bill," he said.

Arden Farhi contributed to this report.