Members of conservative groups around the US are rallying to head off the nomination of US Attorney General Alberto Gonzales to the Supreme Court.
Alberto Gonzales could become the US first Hispanic top judge
Mr Gonzales has been tipped as a likely candidate for the vacancy after Sandra Day O'Connor announced her retirement from the nine-member court on Friday.
Mr Gonzales, a close ally of President George W Bush, would be the first Hispanic to sit on the court.
Mr Bush is not expected to announce his choice until after the G8 summit.
He is facing growing calls to appoint a centrist to replace Ms O'Connor - the first woman to serve on the Supreme Court.
Last week, a delegation of conservative lawyers met the White House chief of staff to warn that appointing Mr Gonzales would divide conservatives, the New York Times reports.
Paul M Weyrich, chairman of the Free Congress Foundation, said he had told administration officials that nominating Mr Gonzales would divide the president's supporters.
"We have let the administration know through whatever channels we have that Gonzales would be an unwise appointment because of the opposition of some of the groups," he said.
He said some groups would actively oppose Mr Gonzales, while "others like the Southern Baptists and myself would simply not help".
The conservatives who oppose Mr Gonzales' nomination say he is too moderate and that his views on issues such as abortion and affirmative action are not far enough to the right.
"We would oppose him because we don't believe he has a philosophy that we can determine. We are not enthused," Tom Minnery of conservative advocacy group Focus on the Family told the Washington Post.
"He is someone who is apparently still developing his philosophy, and that's not good enough," Mr Minnery added, citing Mr Gonzales' "lack of open commitment to interpret the constitution as it was written".
Democratic senators have said they will oppose a conservative nominee.
Mr Gonzales, who is making a surprise visit to Iraq, has said the criticism does not affect him.
"Many of the people speaking probably don't have all the information about prospective nominees. What's important is what the president of the United States thinks about me," he said.
"That's evident by the position he has asked me to fill [as attorney general]."
Mr Gonzales was in Baghdad to meet US and Iraqi officials for talks on efforts to build an Iraqi judicial system.
He said he also wanted to show support for US soldiers on the Independence Day holiday weekend.
The Supreme Court judges - appointed for life - have the final say on US law and justice.
Mr Bush has said he will choose a nominee 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.