The American Conservative is definitely socially conservative and, if not exactly fiscally liberal, at least much more sympathetic to economic redistribution than mainstream conservatism. But it is more composed of opinion pieces than of news reports, so I don't know if it works for way you want.

As others suggested, Vox could be a good choice for a left-leaning news source. It has decent summaries of "everything you need to know about X" (where X = many current news stories).