In a speech on the Senate floor, Udall called the deal, which was also opposed by one Republican, "a step too far" because of the effects it will have on the national debt.
"Days after the most substantive national conversation we've had about addressing the debt," Udall said, "the debate suddenly has turned to extending tax breaks for millionaires and billionaires that - alone - will cost $700 billion over the next decade."
Udall says he hopes the bill will be amended to alleviate the effects on the country's debt.
The deal would extend the Bush tax cuts, which passed in 2001 and were set to expire in 2011, by two years. In exchange, Republicans agreed to fund unemployment insurance benefits for 13 months
The deal, which was brokered behind closed doors last week, is a compromise between the Democrats' position that the tax cuts be allowed to expire for those making more than $250,000 per year, and the GOP stance that they be permanently be extended for all tax brackets.
House Democrats resolved not to bring the legislation to the floor last week, but have since signaled that they will consider the Senate bill.