Republicans now have approximately a one-in-four chance of winning enough Senate seats in the Nov. 2 elections to claim an outright majority of the chamber, FiveThirtyEight’s latest forecasting model shows.

That the composition of the Senate is in doubt is not a new development; the model had assigned Republicans better than a one-in-five chance of claiming the chamber upon its debut at The New York Times two weeks ago. Nevertheless, nearly every day now seems to bring another sour piece of polling news for the Democrats.

Today, for instance, a poll for The Washington Post showed Republicans with a 13-point lead among likely voters on the generic Congressional ballot, which would imply a potentially catastrophic outcome for Democrats. Although the polling trend is not always uniform or predictable — Gallup’s generic ballot poll, which had given Republicans a 10-point advantage last week, now shows the two parties running evenly — the Democrats’ hopes for a spontaneous political recovery this summer now appear to be dashed.

Although the generic ballot is used to help calibrate FiveThirtyEight’s Senate model, most of its inputs are polls of individual Senate races. There, the news is somewhat more mixed. Although polls have come out in the last two weeks showing the Republican nominee in Kentucky, Rand Paul, with an increasingly large lead, and Pat Toomey, the G.O.P. nominee in Pennsylvania, with an expanding advantage over his Democratic opponent, Representative Joe Sestak, a recent poll in Colorado showed the Democratic incumbent, Michael Bennet, with a slight lead. And the model now regards Harry Reid as a slight favorite to retain his seat in Nevada, which was not the case two weeks ago.

Also, although it has become easier — perhaps more than ever — to envision a Republican path toward taking over the Senate, they still remain underdogs and have, in essence, two significant hurdles to clear. The first hurdle is purely statistical: polls are relatively fuzzy instruments prior to Labor Day, before many voters have engaged with the campaigns. And in the weeks immediately leading up to Labor Day — when many Americans are on vacation — they can be especially erratic. If, in two or three weeks, the polls continue to show clear signs of Republican momentum, their prospects for a Senate takeover will be more robust.

The other hurdle is more tangible: there are a series of competitive Republican primaries, in which candidates supported by the Tea Party are pitted against more moderate alternatives.

In Delaware, for instance, Christine O’Donnell — who has the Tea Party’s support — could defeat Representative Michael N. Castle in the primary there next week. Mr. Castle, Delaware’s former governor and its lone representative in the House, would be a clear favorite against his Democratic opponent, Chris Coons. But Mr. Coons would be favored to defeat Ms. O’Donnell, making Republicans’ prospects of a Senate takeover considerably more remote.

And in the New Hampshire G.O.P. primary next week, Kelly Ayotte, the popular former attorney general, could lose to any of a number of conservative candidates whose general election chances are more tenuous.

A primary victory by Ms. O’Donnell, or a loss by Ms. Ayotte, would echo the outcome in Alaska last month, where Joe Miller, a former United States magistrate judge, surprised the incumbent, Lisa Murkowski, in the Republican primary. (Although some polls have shown Mr. Miller’s Democratic opponent, Scott McAdams, making the race competitive, the model is skeptical that a Democrat can prevail in a state like Alaska in such a difficult cycle for the party.)

On average, over its 100,000 simulation runs, the model projected Democrats with 52.1 seats in the new Senate, and the Republicans 47.5. The totals do not add up to 100 seats because Gov. Charlie Crist, who is running as an independent in Florida, still has a reasonable chance of victory.

Some of the slight improvement in the Republicans’ prospects of a takeover — now pegged by the model at 26 percent versus 21 percent two weeks ago — reflects minor methodological adjustments made to FiveThirtyEight’s model, as well as our having incorporated a handful of polls that were previously missing from our database.

The Senate forecast will be updated approximately once a week, usually on Tuesdays.