Since the DNC, things have been going President Obama’s way in the polls. According to Gallup’s Sunday tracking numbers, the president is ahead 48-45. Meanwhile, a recent Democracy Corps poll (PDF) gave Obama a five-point advantage at 50-45. And he holds a 49-46 lead in the latest New York Times/CBS poll.

Then there are the swing-state numbers from the latest NBC/Wall Street Journal/Marist poll: In Ohio, Obama leads Romney 50-43 (with an even larger favorability gap of 51-40). He’s also ahead by five points in both Florida and Virginia.

There’s been a lot of hype from pundits surrounding these numbers. And they are surely good news for Obama. Nevertheless, it is far too soon to declare this race over. The truth is that Romney remains within striking distance—and to count him out would be a tremendous misstep.

First, not all the polls show Obama with a lead. The Rasmussen tracking numbers for Sunday told a different story than most: They gave Romney a 47-46 advantage.

And even in those polls that show Obama with a lead of several points, it’s important to consider the margin of error. In both the Gallup and Times/CBS polls, Obama’s lead is within the margin of error (three points), and, in the NBC/Journal/Marist poll, the 3.1 percent margin of error means that Romney could be within two points in Florida and Virginia.

In a recent interview, Romney told ABC News that he wasn’t worried about the numbers in Virginia and Ohio. He said, “Well, I’m ahead in a lot of other states, too. I saw one this morning, ahead in Florida, ahead in North Carolina. Gosh, we’re even tied in Wisconsin. These polls are going to bounce around a lot. I don’t pay a lot of attention day to day to which state’s up and which one’s down.”

Though Romney’s dismissive attitude toward the numbers is no doubt masking some concern, his supporters can look to 1980 for hope. In mid-September 1980, Gallup had Carter up 44-40 over Reagan. In fact, until late October—when Reagan asked his famous “Are you better off ...” question in a debate—the polls were not favoring him to win at all, let alone by the landslide that he did.

Though it is not expected that Romney will perform as well as Reagan did in the debates, the 1980 case shows that weirder things have happened than Romney coming back from a five-point disadvantage. We also have to consider the possibility that sustained unrest in the Middle East as well as possible conflict with Iran could affect the numbers. Indeed, there is always time for something unpredictable to happen.

The upshot: While Obama is in the lead, it is far too early to be popping any champagne corks.