Speaking of stimulus money and other federal aid to her state, Granholm said on CNN's "State of the Union" Sunday, "This has been critically important money for us as we make our way through this recession."
McDonnell, while acknowledging the stimulus spending "probably helped a little bit," also said state economic development efforts had helped Virginia, which has a 7 percent unemployment rate compared with the national rate of 9.5 percent. He noted the state has turned down some stimulus money.
The two governors differed sharply on the $26 billion in aid to states passed last week by the Senate. House Speaker Nancy Pelosi, D-Calif., is to call the House into session this week to approve the measure, needed to prevent schoolteachers from being laid off before school starts in September.
"We cannot continue to have all of the states rely on the federal government," McDonnell said. "It has to end soon because the federal government is running out of money. I mean, $14 trillion (in total debt), which is $42,000 for every American, it's an unsustainable level of spending. We cannot continue to be a debtor nation."
He said Virginia had cut state spending $10 billion in the past two years and called for restraint in federal spending. "Spending is out of control at a lot of levels of government. We have to live within our means," he said.
Granholm said she is upbeat but realistic about Democrats' prospects in the midterm elections in November.
"I certainly am not Pollyanna about it," she said. "This is going to be a tough slog, because the situation on the ground of the country is so hard. So there's a lot of anger. There's a lot of anxiety."
She said the elections will present a clear choice: "Do the people want to go back to the [President George W.] Bush kind of policies which, of course, started this whole recession to begin with, or do they feel a sense of progress and momentum, and that things have turned around -- you know, turned the corner?"
Granholm and McDonnell also clashed on illegal immigration, healthcare and same-sex marriage, mainly sticking to their respective party lines.
Celebrity Families of 2014 [PHOTOS]