“If this [NSA phone surveillance] came up to the Supreme Court with this Supreme Court, they would declare it unconstitutional,” Laura W. Murphy, the director of the ACLU’s Washington legislative office, said Thursday at an event hosted by Sen. Rand Paul (R-Ky.), who is considering signing on to the group’s suit.

Some outside experts are less certain. Geoffrey Stone, a University of Chicago law professor who worked at the school with President Barack Obama, said the ACLU’s position is “reasonable,” but he doesn’t see the court issuing a ruling that shuts down the phone surveillance program.

And based strictly on existing Supreme Court case law, says George Washington University law professor Orin Kerr, the group’s arguments are “weak.”

But even skeptics of the ACLU’s chances concede the potential for progress. Snowden’s leaks may not lead to a wholesale dismantling of the NSA’s dragnet surveillance efforts — but the revelations could force the high court to reevaluate its interpretations of privacy law.

And this time around, says Kerr, “the ACLU’s goal is probably to get discovery” — to force the government to declassify more information about the programs — “not to win.”