The House approved the resolution on Wednesday. Voter ID bills have already died this session.
Because the regular deadline to file bills has passed, it took two-thirds approval of both chambers to file a new bill.
Eight senators voted Friday against allowing a new ID bill to be filed.
Supporters say requiring voters to show a driver's license or other identification will bring integrity to elections.
Opponents say ID could be used to intimidate some people, particularly older black voters who once had to pay poll taxes.
The movement to revive voter ID came a day after Gov. Haley Barbour signed a comprehensive election bill that did not include identification provisions.
In signing the bill, Barbour called for putting ID into law. Barbour has commended lawmakers for giving ID another chance before the session ends May 9.