Does judicial review give the Judicial branch of the US government the power to veto legislation?

Answer

The judicial branch does not have the power to veto any legislation; however they can use judicial review to label properly challenged legislation unconstitutional. "Properly challenged" means someone who has been directly and significantly injured by the legislation files suit in court, and the case is eventually appealed to the Supreme Court. If a law is never challenged, the Supreme Court has no way to declare it unconstitutional.

A good way to remember this is a football game. The two teams represent the executive and legislative branches and as they are fighting to pass laws and veto laws the judicial branch (the referees) are making sure the players are following the rules.