McDonnell and House Speaker William Howell, R-Stafford, blocked legislative attempts this year to create a state-based exchange.
But Saslaw said "Virginians deserve an exchange that suits their specific needs, not a one-size-fits-all solution from the federal government."
McDonnell also has said he opposes expanding the state's Medicaid program, which provides care for the needy, elderly, blind, disabled and poor families with children. The program is funded jointly by federal and state governments.
A handful of states with Republican governors have said they will not expand Medicaid, which means they relinquish an influx of federal funding that goes with it. The U.S. Supreme Court ruled in June that the government could not withhold federal funds for current Medicaid benefits in states that choose not to expand the program.
Virginia was one of the states that challenged the health care overhaul, which was upheld by the U.S. Supreme Court in June.