Republican U.S. Reps. Gregg Harper, Alan Nunnelee and Steven Palazzo cast no votes, while Democrat Bennie Thompson voted for the legislation that passed 257-167 Tuesday.
Nunnelee said in a statement after the vote that out-of-control spending is the reason the country is $16 trillion in debt and the deal adds to the problem.
"Allowing more revenue today and promising to look at cutting spending down the road is the oldest trick in the Washington book. Somehow, the day to cut spending never comes. I cannot support a deal that adds to our spending-driven debt crisis," he said.
Palazzo said the bill added almost $4 trillion to the deficit, contained minimal spending cuts and passed without the support of many House Republicans.
He said the bill "sets the stage for the next crisis by only taking care of two months of sequestration. This may be a deal, but it's no solution."
"I think the bill ... was the result of an honest effort to come together to find a solution to our fiscal cliff problems. But along the way, some lost sight of the goal: real spending cuts, meaningful tax reform and a pro-growth agenda that will help get our struggling economy back on its feet. Congress has grown so accustomed to kicking the can down the road, that government doesn't know how to operate any other way," Palazzo said in a statement.
The measure passed the Senate 89-8 earlier Tuesday, with Republican Sens. Thad Cochran and Roger Wicker voting yes.
Cochran and Wicker called the plan imperfect, but said it would help prevent a tax increase for most Americans.
"There is still work left to do," Wicker said in a statement. "Congress and the president must reduce the federal deficit."
Cochran said in a statement that the legislation "will ensure that the income taxes for most families in Mississippi will not shoot upward this year."
"There is much more work to be done to responsibly implement spending cuts and other measures to reduce the federal deficit and national debt," Cochran said.
Thompson's office declined to comment on passage of the legislation.