As Republicans rush to jam through a tax bill before year-end, their plan faces two major problems, Sen. Chuck Grassley said on Monday.

The Iowa Republican said House and Senate negotiators still need to compromise on the treatment of the alternative minimum tax and state and local tax deductions. A conference committee aims to resolve differences between separate bills passed in the House and Senate and hash out a joint bill that can pass both chambers before Christmas.

"I think I can tell you some problems have come up very definitely with the corporation AMT and even the individual one," Grassley told CNBC's "Squawk Box."

He added that "some compromise has to be worked out" on popular tax breaks used by people in high-tax states like New York, California and New Jersey.

In a last-minute rush to win votes for its tax bill, the Senate added back the alternative minimum tax, which both chambers initially proposed to scrap. The Senate used the measures to pay for other tax breaks that won over skeptical senators.

The AMT makes corporations or individuals pay a minimum tax if tax breaks make their burden too low. The corporate AMT is currently set at 20 percent, and some corporations pay the higher rate after calculating their tax obligations under both the standard corporate structure and the AMT. Since Republicans want to chop the corporate rate to 20 percent from 35 percent, the corporate AMT could affect numerous companies under the proposal.

Businesses swiftly pushed back against the Senate proposal, arguing that it could stifle research and investment. Top House tax writer Rep. Kevin Brady, R-Texas, and House Majority Leader Kevin McCarthy, R-Calif., have slammed the alternative minimum tax.

On the state and local tax deduction side, both bills would allow only up to $10,000 in property tax deductions. House Republicans in high-tax blue states seek more generous tax breaks because the loss of those deductions could raise taxes for their constituents.

Grassley said Monday the "only" solution he has heard is also allowing up to $10,000 in state and local income tax deductions.

Making changes to those measures would spark another dilemma of how to pay for them. Grassley said cutting the corporate tax rate to only 22 percent rather than 20 percent would offset the alternative minimum tax or state and local deduction tweaks. But he said Republicans should chop the rate to 20 percent to make U.S. businesses more competitive worldwide.