VS 2010 does support the new MVC 4, which includes the new Web API.
You need VS 2010 SP1 which you can get through the web platform installer (WPI).
I could not find the MVC 4 in my WPI. Not sure why but you can get it here (http://www.microsoft.com/web/gallery/install.aspx?appid=MVC4VS2010)
The download opens WPI but I needed to close WPI first to get the download to work.
VS 2010 in WPI
MVC 4 in WPI