During the US election, American voters are the most heavily polled in the world, with hardly a day passing this year without a new survey. They almost all pointed to the same conclusion: the 2012 White House race was nip and tuck. At least until now.

The latest polls show Barack Obama opening up big leads in the swing states. With these most important battlegrounds tilting heavily against him, the Republican challenger, Mitt Romney, faces an uphill struggle to find a path through the electoral college system to the White House.

Obama started with an advantage. Look at the electoral college map of the US and you see swaths of Republican red but most of these Republican states have small populations, each delivering only a few electoral college votes.

By contrast, Obama starts with many of the most heavily populated states in the bag: New York, California and Illinois were always going to vote Democratic. Add together all the solid Democratic states and those likely to vote Democratic and Obama starts the election with 237 electoral college votes, just 33 short of the magic number.

For Romney, the route to the White House is tougher. Even with staunch support in the south and midwest, he started the race with only 191 in the bag.

So the race comes down to eight states: Florida (29 votes), North Carolina (15), Virginia (13), New Hampshire (4), Ohio (18), Iowa (6), Colorado (9) and Nevada (6). The bad news for Romney is that as things stand, these offer Obama various routes to the White House. The respected political scientist Larry Sabato shifted several swing states that had been toss-ups over to Obama yesterday, pushing him well over the magic 270 votes needed to win.

Sabato, a Virginia University politics professor, said he was not calling the race because there were still three presidential debates to come, and an international crisis or poor economic numbers could still change everything. “Caution is always in order with almost six weeks to go, yet President Obama clearly leads at the moment,” he said.

If Obama was to take Florida, where polls put him ahead, he would only need one other small state — as small as New Hampshire or Iowa — to remain president. According to the latest state polls, Obama also enjoys a considerable lead in Ohio, a state which no Republican has lost and gone on to win the White House.

If Obama wins both there and Florida, there is no way Romney can come back even if he won all six remaining battlegrounds.

With six weeks to go everything could still change. Other presidential candidates have been trailing in polls and gone on to win.

Ronald Reagan was behind Jimmy Carter in September 1980 but went on to take the lead in October and eventually win easily in November.

So if Romney won Florida — which is not inconceivable — the calculations would begin to look different. North Carolina should also be natural Republican territory.

With those two, Romney would be on 235 to Obama’s 233 and nervousness would seep into Democratic ranks. Virginia, too, is traditionally Republican territory. Obama’s win in the state in 2008 was a surprise and pundits predicted he would find it hard to hang on to.

Although he was raised in Michigan, Romney’s home state is Massachusetts and he has high hopes of taking neighbouring New Hampshire.

Obama losing all the east coast swing states is a theoretical possibility. At that point, Democrats watching the results coming in at Obama headquarters in Chicago would be nervously waiting for Ohio, Iowa, Colorado and Nevada.

But Sabato thinks such a scenario is unlikely. Virginia and North Carolina, according to his calculations, are no longer in contention.

Only Florida and New Hampshire on the east coast and Colorado in the west, a total of 42 votes, are still in play. “Provided Romney wins the three toss-ups, he will then need to pry another 22 electoral votes from Obama. And that will be difficult,” Sabato said.

By arrangement with the Guardian