Going to be great for the pro-Brexit side. No electorate likes it when a condescending imperial Washington tells them how to vote.
Obama is still popular in the UK; certainly more than Boris is. Had it been someone with the popularity of Bush in his last year in office saying that then I'd agree with you, but not Obama who people still respect. Hell, I'm pretty sure that if you polled Tory voters and gave them the option of Obama or either of the three Republican presidential candidates they'd prefer Obama: the only one that I'd be a little unsure of is Kasich but he's irrelevant and doesn't matter.
I think that Boris's remarks won't help him in the future; its the sort of nasty dog-whistle stuff that hopefully won't be allowed to become common place in British politics, at least to the extent that it seems to be in America. Its not going to affect the referendum much though; although I'm in Scotland where referendum stuff is playing second fiddle to the parliament elections at the moment so it could be different in other places.
