Per Bloomberg senior editor for markets John Authers, it appears as though indeed that has been a huge driver of higher stock prices of late:
"It is rather more discouraging to look at what Buckland
thinks may in fact have been driving the market. If we look at Citi’s measure of short covering over the last decade, we find that it hit a peak a week or so ago. It looks very much as though this market rally has been driven by short-sellers, who enthusiastically bet against the market, deciding to take their profits while they still had some. The fact that short-sellers felt the need to do this is an interesting and positive sign — but it does suggest that the confidence that has brought the market this far is built on slim foundations:"
Oh, and by the way, those short-sellers in SP500 futures contracts are far from giving up at this point: