WASHINGTON – President Barack Obama's Supreme Court pick Sonia Sotomayor looked headed for confirmation as Senate hearings wound up on Thursday with some Republicans open to her bid to become the court's first Hispanic justice.

But conservative critics drove home one final dramatic point on Sotomayor's record on race, calling testimony from two Connecticut firefighters who said she had ruled to deny them the right to promotion because of their ethnic background.

Sotomayor took her last questions from the Senate Judiciary Committee, calmly parrying Republican attempts to depict her as liberally biased and unfit for the lifetime job.

I can't think of any greater service that I can give to the country than to be given the privilege of becoming a justice of the Supreme Court, Sotomayor said.

The committee chairman Senator Patrick Leahy said there was little doubt she would be approved by the Democratic-controlled Senate in coming weeks and take her seat when the nine-member court meets at a special session in September.

And ranking Republican Senator Jeff Sessions said Republicans would not seek to block the confirmation vote expected by early August.

I look forward to you getting that vote before we recess in August, Sessions said.

Some Republicans appeared willing to consider a vote for Sotomayor despite fears the 55-year old judge -- raised in the Bronx borough of New York and educated at Princeton and Yale --- was a judicial activist chaffing to imprint the high court with Obama's liberal agenda.

I think and believe you are broad minded enough to understand that America is bigger than the Bronx, said Republican Senator Lindsey Graham.

RACE CASES

Critics have focused on Sotomayor's attitudes toward race, with Republicans hammering at comments in which she said a wise Latina' might be a better judge than a white man.

She has also come under fire for upholding a lower court ruling that permitted the city of New Haven, Connecticut, to junk firefighter exam results that did not produce enough qualified black candidates.

A mostly white group of firefighters who scored well on the test complained they were being discriminated against, and the Supreme Court later overturned Sotomayor's ruling, saying it could open the door to new racial quota systems.

Sotomayor had left the hearing room by the time Republicans called one of their star witnesses against her: Frank Ricci, the chief plaintiff in the New Haven case.

The rules of the game were set up and we have the right to be judged fairly ... not by the color of your skin, he said.

His colleague Benjamin Vargas, the only Hispanic among the 20 plaintiffs in the case, also testified to the panel.

I do not want my sons to think their father became a captain because he was Hispanic and used his ethnicity to get ahead, Vargas said. In our profession, the racial and ethnic make-up of my crew is the least important thing to us and to the public we serve.

Sotomayor has denied mishandling the case and repeatedly said that her only guide as a judge was the U.S. Constitution and established legal precedent.

BATTLES AHEAD

Throughout the hearing, Sotomayor followed tradition and deflected questions about her position on divisive issues including abortion, gun rights and gay marriage, saying it was not appropriate to comment as these might come before her on the court.

If confirmed, Sotomayor would replace retired Justice David Souter as one of four liberals facing five conservative justices under Chief Justice John Roberts.

Republican Senator Charles Grassley said the sparring over Sotomayor's appointment, which divided along partisan lines despite Obama's hopes of building consensus, signaled battles ahead over the judicial branch of the U.S. government.

Republicans on one side, Democrats on the other, seem to be asking different questions, Grassley told PBS television. In the last 10 years, there's been a change in the environment here that is influencing that.

Among the witnesses testifying in support of Sotomayor was New York Mayor Michael Bloomberg, whose own varied public has seen him on both sides of the political aisle.

I strongly believe she should be supported by Republicans, Democrats and independents -- and I should know, because I've been all three, he said.

(Additional reporting by Richard Cowan; Editing by David Storey and Philip Barbara)