There are two ways that could happen. One is through an extended dip in hiring as the recovery falters — a prospect raised by the Labor Department’s latest employment report, which showed payrolls expanding by just 120,000 in March, less than half the average figure for the previous two months. The second danger to Obama comes from a rise in the supply of workers rather than a fall in demand for them. Even if hiring rebounds in the coming months, which is quite likely, the unemployment rate could tick up, presenting Mitt Romney and the Republicans with an opening they have been desperately seeking.

It is the second scenario that has Obama’s advisers concerned. The doomsayers who seized on the March payroll figures as evidence that something really bad is happening to hiring were probably exhibiting wishful thinking. Most economic indicators still show green. Absent another shock to the economy, such as an Israeli military strike on Iran that causes oil prices to double overnight, the prospect is for more steady if unspectacular growth in employment and output.

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One set of payroll figures shouldn’t be taken too seriously anyway. The margin of error in the payroll survey is 100,000, so the economy could well have created as many as 220,000 jobs last month (or as few as 20,000). And the report had some puzzling features. The number of people working part-time plunged, usually a sign of a robust labor market. In some areas, such as manufacturing, job growth held up well. The weakness was concentrated in retail and temporary-help services, where seasonal hiring and firing plays a big role. One possibility, which economists at Goldman Sachs have raised, is that the warm weather over the winter played havoc with the government’s seasonal-adjustment procedures, causing it to underestimate the number of jobs created in March.

None of that means the White House can relax. Last month the number of people in the labor force — people who are working or actively seeking work — slipped by almost 170,000, suggesting that many out-of-work Americans are still so depressed about the economy’s prospects they are giving up looking for employment. The reduction in the labor force explains why the unemployment rate fell from 8.3% to 8.2% despite weak hiring figures.

Over the next few months this trend could well reverse itself. In most economic recoveries, discouraged workers and people who have retired early go back to scouring the want ads, and the labor force expands pretty rapidly. It hasn’t happened this time. A year ago, 64.2% of working-age Americans were working or looking for work. Today the so-called participation rate is lower: 63.8%.

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At some point soon this trend is going to change direction, and it could change pretty dramatically — good news for employers and for Americans who have been forced to sit at home doing nothing. In many ways it’s what we’ve all been waiting for. But boosting the size of the labor force could lead to a jump in the official unemployment rate. In a recent off-the-record conversation, a (very) senior official in the Obama administration acknowledged that it was a very real possibility — and that there wasn’t anything he and his colleagues could do about it.

In December 2007, at the start of the recession, the participation rate stood at 66.0%, more than two percentage points above where it is now. Between here and November, it isn’t going to get to anywhere near that level. But it could easily rise by a few tenths of a percent — bringing the unemployment rate up with it. And as the election campaign intensifies, even a small uptick in the jobless number could have major political consequences. At the White House the monthly job figures will be creating a lot of agita all the way to the election.

This story is from the April 30, 2012 issue of Fortune.