I do think that Romney might underperform with this demographic (though he might overperform with higher-income whites). Neither Obama nor Romney is exactly the dream candidate for appealing to the white working class, though.
Didn't Obama win amongst higher income whites in 2008 and the same for Kerry in 2004(very narrowly)? Although, from what I remember the Republicans did rather well amongst this group in 2010.
McCain won whites over $50 000, 56-43. Mind you, Obama won voters over $200 000, 52-46, but that of course will include non-white as well as white voters (a small percentage, perhaps,at that income level, but highly likely to vote for Obama, so still potentially significant). With the overall population, income groups between $50 000 and $200 000 were all within about three points between the two candidates.