The top Democrat on the House Ways and Means Committee on Wednesday urged Congress not to make the same tax cut mistakes of Ronald Reagan and George W. Bush.

"What we want to be on guard here for [is] what happened in 2001 and 2003 when taxes were cut by $2.3 trillion," Massachusetts Rep. Richard Neal said on CNBC's "Squawk Box."

While the Bush tax cuts were advertised as a boon for everybody, Neal argued the top brackets "did very, very well" and middle- and lower-income Americans only saw "minuscule results."

Regarding Reagan's tax reductions, Neal said those 1980s cuts left the U.S. with huge deficits.

Supporters of the Reagan tax cuts point to the stronger economic growth that followed after years of stagnation during the previous administration.

President Donald Trump and Republican leaders on Capitol Hill believe that Bush- and Reagan-type tax relief would give the current economy a boost.

In a separate interview Wednesday on "Squawk Box," the chairman of the House Ways and Means Committee said every American will benefit from Trump's tax cuts.

The U.S. also will provide "the lowest rates for our businesses in modern history," GOP Texas Rep. Kevin Brady said.

"We want to accelerate the growth because our economy really demands it," said Brady. "We want to create that permanency and certainty for businesses, especially those making long-term decisions and for those we hope will start bringing back some of their investments and jobs and research from overseas."

Trump, who's been attempting lately to win bipartisan support for tax reform, urged Congress on Wednesday to "move fast."

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On Tuesday, at the CNBC-Institutional Investor Delivering Alpha conference, Treasury Secretary Steven Mnuchin said the Trump administration is considering backdating tax reform to boost the economy. He also insisted a tax reform plan will get passed this year, despite the fact that Congress has not yet agreed on a proposal.

Republican Sen. Jeff Flake said he agrees with Mnuchin, telling "Squawk Box" on Wednesday that he believes Congress and the Trump administration can pass tax reform by the end of the year.

"Republicans need to deliver on something. I'm glad to see the president pushing hard for it and I think he's doing it the right way, approaching some of the Democrats as well, who are likely to be with us," the Arizona senator said.

But Flake, who has been critical of Trump in the past, said he doesn't think the president can get the corporate tax rate for businesses as low as 15 percent, however.

"You simply can't go that far without affecting the debt in a negative way," said Flake, who Trump has blasted in recent tweets over a number of issues.

Watch: Rep. Kevin Brady: We will have the lowest rates in modern history