Republican Policy Committee Chairman Luke Messer said Thursday the GOP budget plan is a step toward helping the economy reach 4 percent growth, a level that's necessary to cut the nation's debt.

The GOP is looking to push through a $4.1 trillion budget plan through the House on Thursday as the party looks to set the stage for tax reform. President Donald Trump has predicted his policies, including tax reform, would spur growth of 3 percent.

"We don't want to have a tax cut that doesn't really get the economy growing again because I can tell you this: If we want to pay down the debt and deficit ... the only time we've done that in modern history is when we've had 4 percent growth," the Indiana congressman said.

"Our number one target in these tax cuts should be what's the path to 4 percent growth," Messer said on CNBC's "Squawk Box."

Messer, a member of the House Financial Services Committee, said passing a budget plan this week is important because "it's the gateway to tax reform."

"We'll get a budget passed in the Senate as well and we'll get it reconciled," Messer said. "What happened in health care is not OK. From my perspective, the United States Senate is broken. It's not OK to make promises on health care for seven years and then shrug and walk away when it got a little hard."

Also on "Squawk Box," Rep. John Yarmuth, D-Ky., said the budget process has been like "Alice in Wonderland."

"We have Republicans who are opposed that will vote for it today," said Yarmuth, the ranking Democrat on the House Budget Committee. "We're fighting about the budget because we really believe the Republican budget represents a drastically wrong set of priorities for the American public and government."

The proposal calls for more than $5 trillion in spending cuts over the coming decade, including a plan to turn Medicare into a voucher-like program for future retirees. It would slash Medicaid by about $1 trillion over the next decade and repeal Obamacare.

Regarding tax cuts, Yarmuth said he's concerned the GOP plan would favor wealthy Americans and corporations.

—The Associated Press contributed to this report.

Correction: This story was revised to correct the amount in the GOP's budget proposal. It's $4.1 trillion.