President Obama on Monday nominated Elena Kagan, the U.S. solicitor general and a former dean of Harvard Law School, to serve on the Supreme Court, ending weeks of speculation about who would replace Justice John Paul Stevens, who is retiring. Her confirmation rests with the U.S. Senate, where Republican critics are expected to home in on a position she took on military recruiting on college campuses five years ago.

In 2005, Ms. Kagan, along with several dozen other Harvard law professors, signed a friend-of-the-court brief urging the Supreme Court to uphold a lower-court ruling that overturned the Solomon amendment, a 1994 law that allows the federal government to withhold funds from colleges that bar or limit military recruiting on their campuses....