Well this took me several hours to figure out: chrome will only let you have one download in progress from the same URL at the same time. The second attempt will just hang until the first one is done.
I tried changing the Content-Disposition filename= value at the server side (so that each download gets a different filename), but that doesn't help. But if I ask for http://localhost/foo and http://localhost/bar, it works. (I can also get two downloads at the same time if I do one of them in an incognito window).
Firefox doesn't seem to have this limitation.