Biden seeks Supreme Court nominee advice amid criticism over promise to name Black woman

President Joe Biden began what he has said would be a bipartisan process to pick his Supreme Court nominee, hosting meetings at the White House on Tuesday amid Republican criticism of his history-making move to nominate the first Black woman to the bench.

Biden met with Senate Judiciary Chairman Dick Durbin, D-Ill., and the committee's top Republican Chuck Grassley, R-Iowa, on Tuesday afternoon to consult with them on the nomination and confirmation process. Vice President Kamala Harris, who Biden has said will advise him on his selection, was also on hand for the Oval Office event.

"The Constitution says 'advise and consent, advise and consent,' and I'm serious when I say I want the advice of the Senate as well as the consent," Biden told reporters at the top of the meeting.

"I'm looking for a candidate with character, with the qualities of ... a judge in terms of being courteous to the folks before them and treating people with respect. As well as a judicial philosophy that is more one that suggests that there are unenumerated rights to the Constitution and all new members mean something including the Ninth Amendment," Biden said.

He also reiterated his intention to announce his nominee by the end of the month.

Biden has also tapped former Democratic Sen. Doug Jones of Alabama to be the so-called "sherpa" of guiding his eventual nominee through the confirmation process, a source familiar confirmed to ABC News Congressional Correspondent Rachel Scott. The White House and a spokesperson for the Senate Judiciary Committee declined to comment.

While some in the GOP have criticized Biden's campaign pledge to nominate the first Black woman to the court, arguing all nominees should be considered for their qualifications, Grassley, the ranking Republican on the panel which will oversee confirmation hearings, said he wouldn't enter that debate until he sees the nominee.

"The president makes a nomination. That's his privilege," Grassley told reporters Tuesday.

"I think I'll be courteous to the president and try to answer his questions," he said ahead of his meeting with Biden. "I don't know what those questions are going to be, but I'm going to take the approach that we need somebody that's going to interpret the law and not make a law because that's Congress's job."

Sen. Ted Cruz, R-Texas, meanwhile, doubled down on his belief to reporters that Biden's pledge is "offensive" to Black women and claimed that Democrats are "very comfortable discriminating based on race."

"When Joe Biden throws out a quota that the only people he will consider for this nomination are African American women. He is number one rejecting regardless of merits everybody else, whether they are white or Black or Hispanic or Native American," Cruz said.

White House press secretary Jen Psaki criticized his comments and called out Republican support for former President Donald Trump promising to nominate a woman in 2020.

“Just over a year ago, the previous president also promised to select a woman for the Supreme Court. Not only were there no complaints about choosing a nominee from a specific demographic, from the same corners, but there was widespread praise of now-Justice Barrett on those grounds with Republican lawmakers," she said.

“Take Senator Cruz himself. He had no objection to Donald Trump promising he’d nominate a woman in 2020. Repeat, no objection at all. In fact he praised her on these grounds," Psaki added.

Despite some Republican opposition, the White House has pushed back on the idea of Biden choosing a candidate just to get bipartisan support.

"The president is going to select a woman, a Black woman, who is qualified, who is prepared, who has impeccable experience to serve on the court," Psaki said Monday. "He's going to do that based on her credentials, of course having a discussion with her and not through gaming out the system."

Psaki said Biden will also begin consulting with legal experts and scholars on the decision this week.

As the process picks up, Biden also spoke with Republican Leader Mitch McConnell by phone Tuesday afternoon.

McConnell's office said the GOP leader "emphasized the importance of a nominee who believes in judicial independence and will resist all efforts by politicians to bully the Court or to change the structure of the judicial system." His spokesperson added that McConnell "believes the cornerstone of a nominee’s judicial philosophy should be a commitment to originalism and textualism."

Earlier in the day, Senate Majority Leader Chuck Schumer applauded the president for his commitment to nominating a Black woman to the high court in an earlier floor speech and called on members from both sides of the aisle to embrace his efforts to diversify the court.

"Every single member of this chamber regardless of party should embrace the president's commitment to make sure that our courts and especially the Supreme Court better reflect our countries diversity. And nominating a Black woman as justice is a long-overdue step to achieving that goal," Schumer said. "The more our judges reflect our nation's vibrancy and diversity, the more effectively they will be able to administer equal justice."

Biden has not yet named a nominee but said he anticipates making a formal nomination before the end of February. Supreme Court nominees only require a simple majority of senators to vote for confirmation, which means there is little Republicans can do to block a Biden nominee if all Democrats -- holding 50 seats in the Senate, and Vice President Kamala Harris acting as a tie-breaking vote -- stick together.

No Black woman has ever been nominated or served on the U.S. Supreme Court. Two Black men and five women, in total, have served on the bench. There have been 115 justices.

ABC News' Allison Pecorin and Justin Gomez contributed to this report.