The lobbying over Supreme Court Justice John Paul Stevens’ successor is picking up, as interest groups push from the outside for their preferred candidates and senators prepare to offer their own recommendations to the White House.

With a known list of seven leading contenders for the impending Supreme Court vacancy, the next several weeks are a crucial chance for those outside the Obama administration to influence the president’ pick. Some allies, including Senate Judiciary Committee Chairman Patrick Leahy, D-Vt., and the liberal group People for the American Way, have made their preferences known, while others say they are just getting ready to weigh in.