Interviewed on "CBS This Morning" the morning after voters re-elected Democratic President Barack Obama, McDonnell said Republicans have a very good message for "people of all stripes" about entrepreneurship, small business and opportunity.
But he says the party has to find ways to appeal to broader swaths of voters before election season begins.
Said McDonnell of Tuesday's results: "We are going to digest this over time."
Exit polls show Obama was propelled to a narrow victory over Republican Mitt Romney with strong support from blacks, Latinos and women. Obama also won McDonnell's state of Virginia.