US President George W Bush is facing growing calls to appoint a centrist to replace Sandra Day O'Connor - the first woman to serve on the Supreme Court.
Justice O'Connor often held the balance in the US Supreme Court
Democratic senators said they would oppose a conservative nominee.
Mr Bush has said he will select a replacement that the nation deserves and "Americans can be proud of".
Ms O'Connor, 75, has often cast the deciding vote on the nine-member court, leading some US commentators to call her the most powerful woman in America.
She announced her wish to retire on Friday - becoming the first Supreme Court justice to do so since 1994.
Speculation has mounted that Mr Bush will nominate a conservative to the court in an effort to tilt the balance of opinion on the bench.
Ms O'Connor - a former Arizona politician - was nominated by President Ronald Reagan and took up her seat in 1981.
Democratic Senator Christopher Dodd urged Mr Bush to follow Reagan's example in making his choice.
"Ronald Reagan was arguably the most conservative president of our time and he chose someone who was confirmed with a vote of 99-nothing," Mr Dodd said.
"That's the standard."
Senator Edward Kennedy said Mr Bush could expect opposition if he chose a conservative.
"If the president nominates someone who threatens to roll back the rights and freedom of the American people, the American people will insist we oppose that nominee, and we will do so," Mr Kennedy said.
The White House said Mr Bush was studying the possible candidates.
The president said he would be "deliberate and thorough" in this process.
"The nation deserves, and I will select, a Supreme Court justice that Americans can be proud of," Mr Bush said.
"The nation also deserves a dignified process of confirmation in the United States Senate, characterised by fair treatment, a fair hearing and a fair vote," said the president in a reference to possible clashes in the upper house.
According to reports, both camps have amassed record sums to spend on adverts promoting or attacking candidates for the vacancy.
Brian McCabe, president of the conservative pressure group Progress for America, said Mr Bush's choice "deserves genuine consideration - not instant attacks".
Ralph Neas, of the liberal organisation People for the American Way, described the nomination process as "a crucial test" for Mr Bush.