Conventional wisdom holds that it is tough to beat an incumbent president. In a broad sense, that is true: 25 incumbent presidents have stood for reelection; only 9 have lost.

But there is a remarkable underlying pattern in American presidential history: while the United States has elected 16 presidents to second terms, in 15 of those cases, the president was reelected by a wider margin than he won in his first-term election.  (The outlier: Woodrow Wilson was re-elected in 1916 by a razor-thin margin in what was essentially a referendum on whether America should enter World War I.  His campaign theme: “He kept us out of war.”  Eleven weeks into his second term, at Wilson’s urging, the U.S. declared war against Germany.  Fascinating history. But I digress.)

There is a lesson in that wider-margin-required-for-reelection statistic.  Second term presidential candidacies are ultimately a thumbs-up/thumb-down verdict on a president’s first term in office.  Either the first term has been successful enough to win over even some of those who voted against the President the first time around, or the President loses.  The question in the minds of voters—especially of those who did not vote for the incumbent the first time around—boils down to: “Do I want four more years of this?”

And in the case of President Obama, who won 53% of the vote last time out, it’s hard to see what segments of the electorate would be clamoring to answer that question in the affirmative at all, let alone in higher percentages than he received in 2008.  His job approval numbers are far below that 53% level already.

Obama’s 2008 margin of victory was 7%.  Now, let’s assume that 2008 Republican voters remain Republican; if just 1 in 13 Americans who supported Obama switch their vote, he loses.  And if he can’t repeat the enthusiastic turnout numbers from various demographics he won in 2008, he’s in even bigger trouble.

Ready for some campaign arithmetic?  Let’s look at those demographics.  First, Obama ’08 spurred record turnout of black Americans—and an all-time high of 13% of ballots cast—who voted for his historic election at an appropriately historic rate of 96%.  Both those numbers will be nearly impossible to duplicate—after all, re-electing the first black president isn’t exactly as monumental as electing him the first time.  Furthermore, Obama’s gay marriage endorsement hurts him in the culturally conservative black community, and astronomical unemployment rates, especially for young black men, aren’t going to help.  If black turnout drops from 65% to a more normal 58%, and Obama’s vote drops to 90%, that 7% margin of victory instantly shrinks to 5%.

The under-30 vote will be another Obama headache.  This demographic turned out in droves for Hope and Change, making up 18% of the total vote, and voting more than 2:1 for Obama—worth more than 6 points of Obama’s 7-point margin.  As they’ve graduated into a terrible job market, the under-30 crowd won’t repeat either that turnout or that endorsement of Obama.  If 1 in 3 of that group’s Obama voters switch sides, that entire 6-point Obama advantage disappears.

The Jewish vote likely presents still another hurdle for Obama.  Jews make up close to 4% of the overall vote (due to ridiculously high participation rates).  Jews voted 78%-22% for Obama, accounting for 3 of Obama’s 53%.  But Obama’s difficult relationships with Israel and the U.S. economy have disillusioned many Jewish voters.  If even 1 out of 3 of those Jewish Obama votes become Romney votes, another 2 points are erased from Obama’s 2008 7-point victory.

Whether the demographic is military veterans, white working class voters, soccer moms, Catholics, Mormons, or Evangelicals, the pattern repeats.  Who is going to vote for Obama in higher numbers than they did in 2008?

Two new polls should be particularly worrisome for Obama.  Gallup reported yesterday that across 12 swing states, Romney voters are more likely to be “extremely enthusiastic” about voting by an 8-point margin.  And the Hill reported its new survey results yesterday showing 1 in 5 self-identified Democrats saying that the country has changed for the worse during the Obama administration. Overall, 56 percent of all likely voters see the changes to the country since Obama took office as negative, versus just 35 percent who view them positively.

“Do I want four more years of this?”  In the face of a limping economy, exploding deficits, and America’s increasingly precarious position on the world stage, it’s hard to believe that Obama can get even all of his own 2008 voters to answer that question in the affirmative, let alone a chunk of those who voted Republican last time.

Only nine incumbents have lost bids for reelection.  But if America continues its pattern of only reelecting presidents by a wider margin than that of their first term, Obama is about to become number 10.