Gingrich on Tuesday said the former eBay chief executive advocates for the right tax policies and is committed to tackling welfare reform, one of his top issues.
California has a 12.6 percent unemployment rate and faces a $19 billion budget shortfall through June 2011.
Whitman built an early 50-point lead over state Insurance Commissioner Steve Poizner, but a poll last week shows her lead has shrunk to 9 percentage points.
Whitman is trying to boost her conservative credentials ahead of the June 8 primary with endorsements from high-profile Republicans such as Gingrich, who led a Republican surge in 1994. Former Vice President Dick Cheney also has endorsed her.