Representatives of the families, who oppose lifting the 19-year-old cap, hand-delivered a request to speak with the Republican governor about the bill.
The General Assembly has passed a bill to repeal the purchase limit, imposed at a time when Virginia was a notorious supplier to East Coast gun-runners.
Gun-rights groups say the legislation is no longer needed because buyers are subjected to criminal background checks, which was not the case when the limit was imposed. Opponents contend it will contribute to gun violence.
McDonnell, who voted for the cap as a delegate but vowed to lift it as a gubernatorial candidate, has said he would sign the bill. The deadline for doing so is Tuesday.
His spokesman, Tucker Martin, declined to comment on plans for the telephone conference.