Sen. Bill Cassidy, R-La., accused President Biden of abandoning true unity for a "patina of unity" and said the president failed to reach out to his group of bipartisan centrist senators before releasing his $1.9 trillion coronavirus stimulus proposal earlier in January.

Cassidy is among ten Republican senators who proposed an alternative $600 billion coronavirus relief package on Sunday.

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"We're targeted to the needs of the American people, treating our tax dollars as if they're our tax dollars not just money to spend," Cassidy told "Fox News Sunday." "If you say you want bipartisanship ... and then you have a budget reconciliation which is chock-full of payouts to Democratic constituency groups ... you don't want bipartisanship, you want the patina of bipartisanship."

Cassidy claimed that Biden did not even try to work with his bipartisan group of senators.

"The President's team did not reach out to anybody in our group, either Democrat or Republican when they fashioned their proposal," Cassidy said. "So if you want unity, if you want bipartisanship, you ought to start with a group that's shown it's willing to work together for a common solution. They did not."

In this Jan. 11 file photo, pre-kindergarten teacher Angela Panush reads a story to her students at Dawes Elementary in Chicago. (Ashlee Rezin Garcia/Chicago Sun-Times via AP, Pool File)

In this Jan. 11 file photo, pre-kindergarten teacher Angela Panush reads a story to her students at Dawes Elementary in Chicago. (Ashlee Rezin Garcia/Chicago Sun-Times via AP, Pool File)

Cassidy said the senators' proposal matches Biden's $160 billion pledge to fund vaccinations and includes $20 billion "to get kids back to school." Cassidy and his fellow Senate Republicans Susan Collins of Maine, Lisa Murkowski of Alaska, Mitt Romney of Utah, Rob Portman of Ohio, Shelley Moore Capito of West Virginia, Todd Young of Indiana, Jerry Moran of Kansas, Mike Rounds of South Dakota, and Thom Tillis of North Carolina sent Biden a letter on Sunday.

"In the spirit of bipartisanship and unity, we have developed a COVID-19 relief framework that builds on prior COVID assistance laws, all of which passed with bipartisan support," they wrote. "Our proposal reflects many of your stated priorities, and with your support, we believe that this plan could be approved quickly by Congress with bipartisan support."

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Cassidy said direct coronavirus relief payments need to be more targeted.

"Above a certain income level, that money's not spent ... doesn't stimulate the economy," he said.

Biden said his proposal would speed the nation’s COVID vaccination program, boost coronavirus testing capacity to help reopen businesses and schools and provide for $1,400 stimulus checks for Americans.

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Biden labeled it his "American Rescue Plan."

"We not only have an economic imperative to act now -- I believe we have a moral obligation," Biden said during a televised address on Jan. 14.

Fox News' Paul Steinhauser contributed to this report.