The concern was raised in December after former House speaker Newt Gingrich failed to qualify for the March presidential ballot and wanted to stage a write-in campaign.
Virginia allows write-ins for general elections, but not primaries.
A final vote is expected Friday before the bill heads to the Senate.
Virginia requires candidates to collect 10,000 signatures, with at least 400 from each of the congressional districts.
Gingrich’s campaign told state officials it had submitted 11,050 signatures. But a Richmond area firm hired to collect them turned in 1,500 signatures that appeared to be signed by the same person.
Only former Massachusetts governor Mitt Romney and Rep. Ron Paul (Tex.) will appear on the Virginia primary ballot.
Gingrich and other GOP candidates, including former Pennsylvania senator Rick Santorum, sued to get on the ballot but a judge ruled against them.
On Thursday, the House also passed a bill by a vote of 71-28 that would change the date of the primary for federal offices to the day of the presidential primary every four years.
This year’s presidential primary is slated for Super Tuesday, March 6.