President Barack Obama could make history with his second nominee to the U.S. Supreme Court by nominating another woman to the high court, a decision many female Senators said they would welcome.

“I would think that would be an excellent idea,” Sen. Mary Landrieu (D-La.) said. “We’ve had what, three women in the whole history of the country? We’re more than 50 percent of the population.”

While Obama is expected to select his high court pick any day now, White House officials continue to dodge questions about when to expect an announcement.

The president will announce his choice “in due course,” White House Press Secretary Robert Gibbs said Wednesday. “I’m not going to get into characterizing where we are in the process, except to say that the president is in the midst of reviewing a number of very impressive candidates.”

Obama and Vice President Joseph Biden have personally met with and interviewed four potential nominees over the past week: Solicitor General Elena Kagan and federal appeals judges Merrick Garland, Sidney Thomas and Diane Wood.

Other female nominees whose names have been floated include Homeland Security Secretary Janet Napolitano and Michigan Gov. Jennifer Granholm (D). There has been some speculation that Obama may be preparing to tap another woman to join justices Ruth Bader Ginsburg and Sonia Sotomayor.

If Obama were to nominate another woman and the Senate confirms her, it would mark just the fourth woman who has served on the court in history, joining Ginsburg, Sotomayor and retired Justice Sandra Day O’Connor. Additionally, it would be the first time that three women have served on the court at one time, bringing the court much closer in line to the nation’s demographic makeup.

“I absolutely think it would be appropriate to add another woman’s voice to the court. … Decisions are best made when everyone’s voices are represented at the table, especially the highest court in the land,” Sen. Debbie Stabenow (D-Mich.) said.

Beyond a better reflection of the nation’s demographics, Landrieu also noted that over the past several decades women have entered the legal profession in droves and now outnumber men in law school graduation rates. “It’s been a real sea change in terms of the depth of the pool of talent,” she said.

National Republican Senatorial Committee Chairman John Cornyn (Texas), who serves on the Judiciary Committee and was a member of the Texas Supreme Court, agreed. “There are a lot more women lawyers these days,” Cornyn said. “There are a number of highly qualified [women], including Diane Kagan and Elena Wood.”

However, some female Democratic Senators said that while they would welcome another woman on the court, they believe it’s more important that Obama chooses a qualified candidate who will make “sure the court remains focused” on issues such as fairness, Sen. Barbara Boxer (D-Calif.) said.

Boxer, who prior to Sotomayor’s nomination in 2009 joined Sen. Olympia Snowe (R-Maine) in urging Obama to pick a woman, said she ultimately wants the White House to pick “the strongest person. If it is a woman, wonderful. But if it’s a man … who brings together the progressive side of things, then I’ll certainly support that,” she said.

On Wednesday, the president also met with influential Judiciary Committee Republican Sens. Kyl (Ariz.) and Orrin Hatch (Utah) to discuss the nomination process, among other topics. Hatch later urged the president to pick a consensus candidate.

“It shouldn’t be someone who substitutes their own personal views for the law of the land, and who refuses to follow the Constitution of the United States. A judicial activist would be a poor and unnecessarily divisive choice at any time,” Hatch said in a statement.