Trump blamed the Tennessee Republican on Sunday for the Obama administration's nuclear deal with Iran, and suggested that Corker actively pursued a re-election endorsement from Trump and a top ranking Cabinet post.
In response, Corker blasted the White House, tweeting that it had become an "adult day care center" and saying that someone "missed their shift."
"Corker's a grown up. He can have a fight with the president," said Norquist, founder and president of Americans for Tax Reform. "He has already done the negotiating that he's focused on to try, in his view, limit the size of the tax cut."
"He's a serious guy in terms of wanting economic growth," Norquist added in an interview on "Squawk Box."
The war of words came as the GOP faced the daunting task of tax reform. Corker has stated he cannot support tax legislation that adds to the annual federal deficit.
Jared Bernstein, former chief economist and economic policy advisor to Vice President Joe Biden, told "Squawk Box" that Trump's tax reform plan doesn't close enough loopholes and skews more benefits to the wealthy.
Bernstein also argued against the president's claim that tax cuts will result in economic growth. "There is no correlation between tax cuts and economic growth," he argued.
Trump has predicted his policies, including tax reform, would spur growth of 3 percent.