Where better right now than Washington DC to savour the joys of baseball? On Thursday evening, our once woeful Nationals became the capital's first major league team to clinch a place in the play-offs since 1933, when Franklin Roosevelt had been barely seven months in the White House, and the hometown Senators ultimately lost the World Series to the New York (now San Francisco) Giants.

The morning after was glorious, too, and here at the stadium of the Potomac Nationals, the franchise's minor league affiliate in suburban Virginia, the visitor was FDR's distant successor. Fêting him were some 12,000 exuberant supporters, not a few of them sporting scarlet Nats caps, chanting: "Four more years, four more years". Ah, Barack Obama grinned as he bounded to the microphone: "Sunshine, a nice little breeze in the air – it feels good to be at the ball park."

Indeed it did, and not just because of what the Nationals had achieved a few hours earlier. To put it mildly, campaign rallies can be repetitious: the same stump speech only occasionally retooled, the same packaged razzmatazz, capped by the candidate's obligatory glorification of the United States as the greatest country in the history of the world (and doubtless the universe as well). But rallies can also be highly revealing. At the G Richard Pfitzner Stadium, the crowd was rocking, and Obama with them. There was no mistaking the changed mood. After long months of uncertainty, the Democrats now genuinely believe they're going to win on 6 November.

Largely responsible for this transformation, of course, have been the recent travails of Mitt Romney. Last week was surely his worst of the campaign so far. It began with the reports of infighting among senior staff, always a sure sign that things are not going well. That was quickly followed by the leak of the secretly filmed video of a $50,000-a-plate fundraising dinner in Florida, where candidate Romney confided that 47 per cent of Americans were scrounging parasites who considered themselves to be "victims".

The media may have exaggerated the impact of that gaffe (name the modern presidential candidate of either party who has navigated a campaign without some such blunder). But there can be little argument with the string of polls beforehand that showed Romney trailing not only nationally, but also in almost every swing state, of which Virginia is among the most important. Even on the economy and deficit reduction, long regarded as his trump issues, he no longer has an advantage.

Alarmingly, Romney's problems seem to have spread to other Republican candidates. In at least three closely watched Senate races – in Wisconsin, Massachusetts and here in Virginia – Democrats have suddenly snatched a lead. A few weeks ago, Republicans were pretty sure of making the net gain of four seats to give them control of the Senate. As matters now stand, they won't. And they could conceivably lose their majority in the House as well.

No wonder the intra-party sniping at Romney has been enough to provoking a remarkable outburst from his wife. "Stop it," Ann Romney told Republican critics. "This is hard. You want to try it? Get in the ring." She might however, bear in mind that the brutality of presidential campaigns offers at least some preparation for the even more brutal demands of the job itself. A quiet word with Hillary Clinton, who endured much worse and for much longer, than anything experienced by Mrs Romney, would be in order.

Most worryingly, perhaps, her husband seems to be losing the money wars. Throughout the summer Democrats braced for a post-convention advertising blitz, courtesy of Romney's supposed financial juggernaut. The blitz, however, has not materialised. In August, even before his highly successful convention in Charlotte, Obama out-raised his rival, who that month was forced to take out a $20m (£12.3m) loan as funds raised during the primary season ran out. Republicans, of course, have their Super PACs, financed by wealthy sympathisers. Among smaller grassroots donors, though, Obama is winning hands down.

But Friday's rally was a reminder that, for all Romney's obvious shortcomings, his wounds are not entirely self-inflicted. The Obama magic of 2008 is gone, crushed by grim economic and financial reality. But this President remains a formidable politician. Yes, he lacks Bill Clinton's gift of empathy (who doesn't?). He was also probably naive in his hopes that Republicans in Congress might show a modicum of reasonableness.

But he's run a competent and notably scandal-free White House. Obama makes few serious mistakes, and those he does he quickly learns from – which does not augur well for Romney in the forthcoming presidential debates, widely seen as the Republican's best (and probably last) chance to turn things around. Finally, he has at his disposal as well-honed and ruthless a campaign organisation as any in recent memory.

Team Obama was near flawless four years ago, and this time around has been the same. The secret lies in a combination of smart strategy, super-smart technology and a potent ground operation. The former was especially evident in the pre-convention demolition job carried out on Romney. Just as George Bush/Karl Rove managed to brand his opponent John Kerry as an elitist and a flip-flopper in 2004, so – from the moment Romney became the likely nominee, and before he could move back to the centre from the conservative posturing required in the primaries – the Obama operation painted him in the colours of its choice: as a callous and out-of-touch corporate raider who enriched himself at the expense of the lost jobs of ordinary workers. Romney's failure to hit back at once, and his persistent evasiveness about his tax arrangements, didn't help. But when offered the opportunity, Obama's people made the very most of it.

Meanwhile the Obama campaign, based like the 2008 operation in Chicago, boasts technology enabling it to micro-target voters as never before, while volunteers in the field make sure that once successfully targeted, voters are fed information on the issues that matter most to them. At the ballpark on Friday, the results were plain to see. Not only have Democrats managed to bridge the "enthusiasm gap" that helped Republicans to their historic win in the 2010 mid-terms, and then some. The targeting has also helped consolidate Obama's strength among the constituencies most likely to carry him to victory in November: female voters, blacks and Hispanics. The crowd was a rainbow gathering in which women easily outnumbered men.

Virginia's entry into the select group of "battleground" states alongside Florida and Ohio is a recent affair. Before Obama, the last Democrat to carry the Old Dominion, the linchpin of the Confederacy, had been Lyndon Johnson in 1964. But the explosive growth of the Washington suburbs – "occupied Virginia" as some old timers call them – and a corresponding influx of more liberal voters have transformed the landscape. Obama leads there by six or seven points, thanks mainly to a huge 20 per cent advantage among women. The pattern is similar in other swing states, and it is unlikely to change greatly before 6 November.