I can appreciate the fact that fawning, sycophantic, and generally embarrassing conservative cheerleading has helped bolster Reagan's image in the wake of his presidency. I also realize that Reagan, more than any modern leader, is the only GOP figure who's claimed by every wing of the Republican Party as their own -- from New England moderates to Deep South far-right conservatives.
But up against FDR, how is this even a contest? Reagan's economic policies were largely unsuccessful; propaganda notwithstanding, he was not responsible for winning the Cold War; his White House traded weapons for hostages in Iran-Contra; and no president before or since oversaw a White House filled with so many officials convicted of felonies (32, not including 30 who resigned in disgrace or fired following charges of legal or ethical misconduct).
However, I must point out one thing: this is a poll of who was most influential, not who was most effective. Reagan, while not particularly effective, was quite influential, and in fact, the image of Reagan, and Reaganism -- his penchant for belittling his opponents with a never ending stream of wisecrack non sequiturs -- still maintains a deathgrip on the Republican Party, and to a lesser extent, the media itself. The image of Democrats as a bunch of soft-on-everything, elitist, head-in-the-sky pansies originated with Nixon, but it was under Reagan that it really took hold in the nation as a whole.
If you look at Reagan's influence on policy, he left a mark there, too. Clinton's presidency was essentially a defensive battle against the policy prescriptions of the extreme right. Welfare reform, entitlements, deregulation of industry -- the whole "the era of big government is over" thing -- were all Reagan initiatives, that he himself was unable to enact, but that had huge residual staying power, particularly when the Republicans were able to assume control of Congress. And of course, we saw the real influence of Reagan once the Republicans took control of everything, and a swaggering buffoon was able, in a few short years, to ride the country headfirst into the ground, feet in the stirrups of Reagan campaigning and Reagan policies.
Was Reagan as influential as FDR? That's absurd. Even to this day, we're still operating in FDR's world, as we make our retirement plans with FDR programs like Social Security and FDR-inspired programs like Medicare at the center; and our entire concept of what government is and should do has been permanently changed by FDR's 14 years in office. And it was FDR who put an end to isolationism on the international front, got the ball rolling on the UN -- he shaped much of, not just U.S. policy, but world policy, both directly and indirectly through his chosen successor, Truman. Reagan chose no successors, while those who won in his name did abysmal jobs -- in fact, this Bush has done a wonderful job of pushing the country away from the policies Reagan was ostensibly for. No way was Reagan even close to as influential as FDR was -- and that's leaving out the concept of effectiveness. I'm perfectly content to call Reagan the second-most influential president of the 1900s, but only if you keep in mind the notions that 1) in this case, it's rather like being the second tallest guy on Kareem Abdul Jabbar's high school basketball team; and 2) "influence" can be a good thing -- or quite a bad one, and still be influence all the same.