No.

First, the recession you're thinking of wasn't even technically in the 1970s, though it followed close on the heels of the 1979 energy crisis. Peak-to-trough, the recession that likely contributed to Reagan's victory lasted from January of 1980 to July of the same year. It was both significantly shorter and less dramatic than the late-2000s recession, though it should be noted that it was followed in 1981 by a "double-dip" recession which was much more serious (but still not on the level of the Great Recession).

During the 1980 recession, the unemployment rate maxed out at 7.8%, compared to 9.5% during the late-2000s recession. Real GDP contracted by 142.02 billion in 2009 dollars for a loss of about 2.18% during the 1980 recession, compared to 533.9 billion in 2009 dollars for a loss of about 3.59% during the late-2000s recession.

Data is from the National Bureau of Economic Research (NBER) and FRED Economic Data of the St. Louis Fed.

EDIT: fixed real GDP links and added percentages for real GDP contraction.