You could simply use the more accurate term of 'center right' JGW. It's O.K. and would be more accurate in a historic and now, thankfully, current sense. I can understand how someone from a managerial class would find comfort in a 'leftists' political positioning going no further than, say, Chuck Schumer or Nancy Pelosi but they would hardly qualify as 'left' by any edjumacated standard.
Your calling the current majority of the Democratic party left would be akin to calling the Tea Party Republicans 'nostalgic' or 'slightly old fashioned'.
By the By, I would disagree with your notion that the democratic party is the responsible party of the economy. Unless you ignore Dollar Bill Clinton deregulating the banking industry leading to the 2008 banking/ housing crises and of which Obama did everything for the banks to make them whole and very little for actual citizens under water. Just saying.