Some Democrats pressed for an estate-tax provision that would set either a 35 percent or 45 percent tax on estates of $3.5 million or more.
Kyl and Democratic Sen. Blanche Lincoln (D-Ark.) had authored a bill in July that called for the 35 percent level.
Senate Budget Committee Chairman Kent Conrad (D-N.D.) said he strongly opposes the deal Obama and Republicans struck on the estate tax. He would prefer to tax estates above $3.5 million at a 45 percent rate, but said significant revisions to the package are unlikely, he acknowledged.
"The one place I am disappointed is on the estate tax, where I believe this agreement goes too far," Conrad said in a statement. "But the President did what he had to do. I applaud him for working with Republicans to achieve a bipartisan agreement."
Rep. Chris Van Hollen (D-Md.) said Wednesday the overall passage of the plan is in jeopardy because of the estate tax, calling it a "bridge too far" for most Democrats.