Mitt Romney returned from his contentious foreign tour to face bleak news in the opinion polls. But one of his first acts was to defend widely condemned comments he made in Jeruslam that appeared to suggest Israel was more economically successful than the Palestinian territories because it has forged a superior culture.

A New York Times/Quinnipiac University poll on Wednesday shows Romney lagging in three important swing states – Ohio, Pennsylvania and Florida – where voters regard Obama as more likely to care about their "needs and problems".

Romney's attempts to play up his business experience have not sat well with many voters, who said he was too focused on making money at Bain Capital, and that did not provide the experience necessary to rebuild the US economy and create jobs.

The Obama campaign has attacked Romney over his years at Bain, saying he profited by shipping American jobs overseas.

Concern about the economy remains the single most important issue. The poll showed likely voters in the three states to be evenly divided on who will handle the economy best, which is not good news for Romney given that he is counting on the recent poor economic figures, including rising unemployment and the low growth rate, to bolster his campaign.

Overall, Obama leads Romney by six percentage points in Florida and Ohio, and by 11 percentage points in Pennsylvania.

Four years ago, Obama won all three states. Romney will probably have to take Ohio and Florida to win the presidency.

"If today were 6 November, President Barack Obama would sweep the key swing states of Florida, Ohio and Pennsylvania and – if history is any guide – into a second term in the Oval Office," said Peter Brown, assistant director of the Quinnipiac University Polling Institute.