The first quick polls after the debate last night pointed to a victory for of Barack Obama against Mitt Romney, 46 per cent to 39 in the CNN survey, 37 per cent to 30 of CBS’s survey and 48 per cent to 31 in the Google Consumer Surveys among registered voters.

It was a new Obama that showed up last night, compared to the Denver debate two weeks ago: tough, aggressive, committed, concentrated, eloquent. Unlike in Denver, Obama did not give way on a single point, constantly counterattacking and repeatedly stating that what Romney said was not true.

You could almost hear the sigh of relief among Democrats. It was a new ball game. The strangely absent president in Denver was a distant memory — “Obama was back!”

Romney was also clearly not as strong as in the first debate, forced on the defensive by Obama’s unwillingness to budge an inch. Several of his answers, on tax policy and women’s issues, but especially on Libya, were weak. On Libya, Romney had to stand corrected by the moderator as to what the president said after the deadly attack on the American consulate.

In addition to these first positive poll numbers for Obama, the fact that the media almost unanimously pointed to Obama’s strong debate will greatly influence public opinion in the next days.

Conclusion: Obama seems to have regained the initiative in the election campaign after the Denver debacle. The question is how much will the debate move the head-to-head polls between Mr. Romney and Mr. Obama?

Nate Silver has a warning on his FiveThirtyEight blog:

“Actually, the instant reaction polls may not be very much help in answering that question. The relationship between the quick-reaction polls and their contingent effect on the horse-race polls has historically been very modest, and has sometimes even run in the opposite direction of what the initial polls suggested. Debates sometimes look different in the rear-view mirror, depending on news media coverage, YouTube and cable news highlights, word of mouth, and subsequent developments on the campaign trail. “

He continues:

“But if you want my best guess: Throughout this election cycle, you would have done very well by predicting that the polls would eventually settle in at an overall lead for Mr. Obama of about two percentage points.”

Silver now puts Obama’s chances to win the election at 64.8 per cent, while the betting site Intrade sets the number at 64.9 per cent, up from 61.7 before last night’s debate.

The third and final debate will take place next Monday. It will be on foreign policy — Obama’s strength and Romney’s weakness — both of which were underlined again in the Libya debate last night.  That speaks to Obama’s advantage, but much can still happen as the campaign moves to a final decision on Election Day.