TEL AVIV—Prime Minister Benjamin Netanyahu’s quest to become Israel’s longest-serving leader has become a referendum on his decades in public life.

The race is tight. Most final polls show a fluid situation ahead of Tuesday’s vote, with Mr. Netanyahu’s main challenger, former Gen. Benny Gantz, drawing slightly more seats with a message focused on voter fatigue, corruption allegations and quality of life issues. But small right-wing parties are forecast to do well enough to put Mr. Netanyahu in a better position to cobble...