Whenever I hear or read Obama on the Middle East, my thoughts dart straight back to a supermarket car park in Virginia just before the presidential election.

Interviewing voters about Obama's impending visit to a very red part of a then very red state, a teen mother told me why she wouldn't vote for him.

"I know he's not a Muslim but he was raised a Muslim," she told me, adding a new twist to the myths swirling around the election.

I thought Obama would find that perception impossible to overcome and he would lose.

I was wrong, of course. 

But the same sentiments will force him to tread very carefully as he tries to do what both Bill Clinton and George W. Bush couldn't: oversee a lasting and meaningful peace for the Middle East.

Obama is keen on dialogue with Iran and there are reports that he wants to open up indirect and low-level channels with groups like Hamas.

It's a red rag to people like my young mum interviewee who lapped up allegations that Obama was the choice of Islamic militants.

And even the most liberal Jewish voters who didn't buy that line may be concerned about exactly how far their new president will go in his pursuit of multilateral talks with the main players in the Middle East.

That said, Obama has been careful to flag up his support for Israel. His visit there last summer caused a storm among Arabs when he said "Jerusalem will remain the capital of Israel, and it must remain undivided."

This may have been a US policy position since 1995 but Obama's strategy for keeping the Jewish vote on side was clear.

And if that's the case, just how far will he depart from George W. Bush's disastrous policy of isolating Hamas and giving almost unequivocal support to Israel?

With no immediate prospect of peace in Gaza, we may find it out pretty soon after 20th January when Obama won't have the luxury of choosing when and how he talks about peace in the Middle East.