"You have the House and the Senate that wants the same thing because they're all running for election in the House in 2018 and a third of them in the Senate. This is the centerpiece, here's what we did."
President Donald Trump has suggested that McConnell should resign if he can't successfully push through the White House's agenda, including tax reform and a "great" infrastructure bill.
On Tuesday, The New York Times reported that Trump and McConnell haven't spoken to each other in weeks, and that their relationship has been conspicuously tense after Trump blamed McConnell for the GOP's health-care failure.
Stocks surged Tuesday after a Politico article said Trump's top aides and Republican congressional leaders have made strides in shaping a major tax overhaul and have "broad consensus" on ways to cut corporate and individual tax rates.
Trump has said the bill could be the "biggest tax cut" in American history.
Norquist, founder and president of Americans for Tax Reform, said the Trump administration's goal of a 15 percent corporate tax rate is possible. He said the White House could run into a few obstacles with the bill.
"There are some limits on how much you can cut taxes for what period," he said. "Some of these tax cuts would be temporary. You can have any tax cuts you want for 10 years under the Senate rules. ... But then in year 11, some or much of it would disappear."