U.S. District Judge James R. Spencer heard arguments Monday in Richmond from attorneys for McDonnell and his wife, Maureen.
They are seeking the dismissal of most of the corruption charges filed against them, as well as separate trials.
The government opposes both requests.
The Republican and his wife are charged in a 14-count indictment with accepting more than $165,000 from Jonnie Williams, the former CEO of dietary supplements maker Star Scientific Inc. In exchange, they would help promote his products, according to prosecutors.
The McDonnells have pleaded not guilty.
A jury trial that is expected to last at least five weeks is scheduled to begin in late July.