Rex Tillerson, former chairmen and chief executive officer of Exxon Mobile Corp. and USA secretary of state nominee for President Donald Trump.
The 56-43 vote on Monday puts Tillerson's bid to be the nation's chief diplomat on track for confirmation later this week.
"They have nothing going but to obstruct", he tweeted.
In addition to voting against the motion to advance Tillerson's nomination, Udall has joined Senate Democrats on a number of measures to condemn and fight President Trump's hateful immigration executive order.
With Republicans controlling the Senate by a 52-48 margin, Tillerson's confirmation is believed to be assured now that Senator Marco Rubio, R-Fla., Sen. A simple majority is required for confirmation of cabinet positions, so any Democratic effort to derail a nominee would need Republican help.
The Senate will hold a flurry of votes on Tuesday, including a confirmation vote for Ms Elaine Chao as secretary of transportation.
"The proceedings in the Foreign Relations Committee for his nomination were fair, exhaustive, and in the best traditions of our committee and the Senate", Corker said.
The Senate Finance Committee was expected to approve Georgia GOP Rep. Tom Price to be health secretary and Steve Mnuchin to lead Treasury.
The Senate's Democratic leader, Chuck Schumer, and several other members of the party tried, but failed, to delay considering Tillerson because of Trump's executive order banning immigration from seven mostly Muslim countries and temporarily halting the entry of refugees.
U.S. Sen. Bob Casey, D-Pa., plans to vote against nominating Rex Tillerson as the next Secretary of State next week, saying the two men have "basic disagreements about the most fundamental issues facing our nation".
Tillerson's confirmation vote is scheduled for Wednesday.