According to moderate Bruce Bartlett, here, who voted for Obama at least once:
"Although the far right’s mythology paints the Reagan years as the triumph of their ideas, the truth is that he governed very much in the moderate tradition of postwar Republican presidents. Reagan raised taxes 11 times, gave amnesty to illegal aliens, pulled American troops out of the Middle East, supported environmental regulations, raised the debt limit and appointed many moderates to key positions, including on the Supreme Court. But he skillfully kept his right flank protected by using thundering conservative rhetoric, even as he violated his own stated principles on a regular basis."