Graham, who is running for president, called for Estrada to provide senators with more information to evaluate his nomination to the U.S. Court of Appeals for the District of Columbia.
A Florida Democrat who could choose to seek reelection next year, Graham has struggled over whether to support Estrada, a Honduran immigrant who would become the first Latino on the court if confirmed.
Democratic senators have staged a filibuster to keep the nomination from coming to a vote. The Republican majority tried to end the delay Thursday but was five votes short of the 60 necessary to cut off debate.
Housing and Urban Development Secretary Mel Martinez issued a statement urging Graham to reconsider his position. Martinez is weighing whether to run for Graham's seat next year, according to published reports.
"The senator's vote today is not in keeping with his long tradition of being supportive of the interest of Hispanics," said Martinez, a Republican. "The action he took is not representative of his Florida constituents."
Graham's vote also drew fire from Florida Republican Party Chairwoman Carole Jean Jordan and Rep. Mark Foley, a Republican who wants to replace Graham. Foley called the vote "a slap in the face to the Hispanic community."
"Sen. Graham isn't only voting against a qualified nominee, he's voting against inclusion," Foley said in a statement.
But Rep. Ileana Ros-Lehtinen (R-Fla.) hinted that even though Graham voted to continue the filibuster, he might support the Estrada nomination when it comes to a final vote. "We're optimistic that we can get Sen. Graham's vote," she said.
The three other Democratic senators running for president -- John Edwards of North Carolina, Joseph I. Lieberman of Connecticut and John F. Kerry of Massachusetts -- have supported the filibuster. On Thursday, Lieberman again voted against ending the debate; Kerry and Edwards missed the vote. All voted to continue the filibuster last week, a vote that Graham missed while recuperating from heart surgery.