The official pointed to a chart we've recreated here:
The basic point is that under Presidents Reagan and Obama spending as a share of the economy climbed, and taxes as a share of the economy fell, during deep recessions. But the officials noted that they picked two years, 1983 and 2010, because they represent similar moments in the business cycle.
If they're right, it portends good things for the U.S. After all, 1984 was "morning in America," and barring unexpected contractionary policies, a similar boom would put the economy on a healthy path toward recovery.
Update: Readers have noted that, because Obama inherited a much larger economy than Reagan, laying their real GDP figures over each other creates the impression that the Obama recovery is more robust than Reagan's was. While the intent of the post is not to compare the magnitude two recoveries -- it's to note the real likelihood that Obama's recovery is in full gear -- it behooves us to point out that Reagan's economy grew by a larger percentage than Obama's from its trough to level at the end of 1983. About 7.4 percent to Obama's 5.9.