White House communications director Kate Bedingfield remained confident Sunday that President Biden's $1.9 trillion coronavirus relief bill narrowly passed by the Senate over the weekend would ultimately reach the president's desk, as the legislation is up for a vote in the House this week where Democrats hold a narrow majority.

In an appearance on CNN's "State of Union," Bedingfield described the bill -- called American Rescue Plan – as a "historic and transformational piece of legislation" that will "cut child poverty in half" by making investments in the child tax credit, fund a vaccine program and get money out to schools to reopen, even with the nation strapped with $28 trillion in debt.

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"This is an incredibly transformational, frankly progressive piece of legislation," Bedingfield told CNN host Jake Tapper, who questioned whether the bill has enough votes in the House to pass. 

House Speaker Nancy Pelosi, D-Calif., can only afford to lose four votes and still send the bill to Biden's desk for his first major legislative win. Progressives in the House have raised concerns about changes to the bill that eliminate the $15 minimum federal wage, lower weekly unemployment benefits from $400 to $300, and limit income eligibility for stimulus checks.

"You heard Sen. [Bernie] Sanders say that this was the best legislation for working people in the modern history of this country," Bedingfield said. "This is a bill that reflects President Biden's belief that the best way to get the economy back on track and get it growing is to invest in working people and middle-class people."

Acknowledging support from Sanders, Tapper pointed out that other progressive Reps. Rashida Tlaib, D-Mich., and Jamaal Bowman, D-N.Y., both have voiced criticism of the legislation.

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And the Senate parliamentarian ruled that the bill's move to raise the federal minimum wage to $15 per hour would violate budget rules.

Some Republicans said they would support amending the federal minimum wage to $10 an hour, and Sen. Joe Manchin, D-W.Va., said he supported an $11 an hour change to the bill.

Despite claiming Biden is willing to work with Republicans, Bedingfield said that the president supports a $15 an hour hike. 

"President Biden supports raising the federal minimum wage to $15 an hour," Bedingfield said. "That is where he stands. That is where he stood for a long time. He believes strongly that people who are in this country who are working full time can make a living wage and not be living in poverty."

"The conversation is going to turn to how we tackle the minimum wage," she continued. "The president is looking forward to working with Congress to determine the best way to do it. What I can say to you right now is the president is committed to raising the federal minimum wage to $15 an hour."

Biden cheered the passage Saturday, brushing off the lack of any GOP support in the Senate or House, and said he hasn't given up on working with Republicans on future legislation. Biden touted the relief provisions in the bill, including unemployment benefits, food aid, vaccination distribution support and the $1,400 stimulus payments. He told Americans they'd be seeing those checks soon.

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Bedingfield reiterated Sunday that Biden’s preference is not to end the filibuster, saying the administration would need to navigate through a 50-50 Senate. She said that although the bill was passed without any Republican support in the Senate, it did receive 75% approval from the American people "including over 50% of Republicans" who rallied behind Biden’s approach.

"We were able to pass this legislation with massive bipartisan support across the country," she said.

Fox News' Marisa Schultz contributed to this report.