“It’s quite likely the left is not going to get what it wants,” said Thomas C. Goldstein, co-head of the Supreme Court practice at Akin Gump Strauss Hauer & Feld and founder of Scotusblog, a well-read Web site. “If you talk about somebody who’s a true liberal, a very strong progressive and a visionary architect of the law and jurisprudence, then you’re talking about somebody like Pam Karlan at Stanford. And nobody is seriously talking about Pam Karlan.”

Image President Bill Clinton with Ruth Bader Ginsburg in 1993. President Obamas court nominees may follow the Clinton model. Credit... Doug Mills/Associated Press

Other favorites of the left who do not appear to be on Mr. Obama’s short list are Kathleen M. Sullivan, who also teaches at Stanford, and Harold Hongju Koh, the dean of Yale Law School, whom the president has nominated to be the legal adviser at the State Department.

“Unless Obama restrains his compulsion toward centrist consensus and appoints real progressives to replace not only Souter but Ginsburg and Stevens, our right-wing court may get even more conservative,” Jeff Cohen, founding director of the Park Center for Independent Media at Ithaca College, wrote on a Web site for progressive commentary, OpEdNews.com.

The four said to be on Mr. Obama’s list are known as liberals if not crusaders, and advocates said they would still generate enthusiasm. Judge Wood, in particular, has attracted favorable attention from the left. Still, Geoffrey Stone, a University of Chicago law professor, who expressed great support for his former colleague, noted that she was an “incrementalist” not inclined to take on broad structural changes in the law.

Ms. Kagan has drawn more mixed reviews on the left because of her support for executive power and what some colleagues said was a tendency to find a middle road.

The White House does not appear to be especially worried about criticism from the left. With an eye to the confirmation battle ahead, it seems happy to embrace the conclusion that Mr. Obama was choosing from a list with more moderate tendencies than many liberals would like to see in the next justice.

Mr. Obama is already taking heat from conservatives for saying he favors appointing someone who shows “empathy,” a word the right views as code for judicial activism.