I think that under $2000 for a studio is going to be quite difficult to find in Cambridge. I paid about $1500 for a studio in Cambridge 6 years ago and that was MIT-subsidized housing (for grad students, unfortunately I don't think they have anything for postdocs). I think finding a cheaper 2 bed is significantly more do-able (could be easily <$1500/person). That being said, there are always occasionally random deals that pop up, but they'll often get snapped up extremely quickly. Places to look include East Cambridge and Alewife, also try looking in Somerville and if you're okay with a longer commute maybe look in like Allston or Dorchester/Roxbury? I know some folks who live there who have insanely cheap (to me as someone who lives in Cambridge) rent.