Kaine's wife, Anne Holton, delivered 30,866 petitions to the State Board of Elections on Monday afternoon.
The Democratic Party of Virginia will verify the signatures. If no other Democrats are certified for the ballot, the Democratic primary will be canceled.
Candidates have until 5 p.m. Thursday to collect 10,000 signatures from across the state, including 400 from each of the state’s 11 congressional districts. Two Republicans — former governor and senator George Allen and tea party activist Jamie Radtke — submitted their signatures earlier this month.
Others in the GOP race include Del. Bob Marshall (Prince William), Hampton Roads lawyer David McCormick, and Bishop Earl Jackson.