I think the leap of logic in the above is in the use of the word “left”, whereas what should be used is “liberals” or “progressives” (or the “poor” or “working class” or “minorities” or “youth") - whose impact on electoral outcomes is not negligible in theory. In practise of course they (liberals) vote on the least evil principle, or they (poor, youth) stay away. So Obama can count on their vote and pander to the “independents” and non-all-out-wacko right-wingers or try to win back the vote of the disenchanted (mostly the youth). The former (pandering) is more reliable.
Further, where from the idea that Obama cannot ignore election results? He was able to resist populist sentiment that elected him to power, to dole out riches to his Wall Street paymasters and steadfastly refuse to punish them in any way for their excess.
Occam’s razor says: Obama is a triangulating neo-liberal.
—ravi