Uploading to Amazon S3 using a signed URL works with curl but not in javascript

I'm trying to upload a file to Amazon S3 using a PUT request. I generate my signed urls using boto. If I do

curl --upload-file test.jpg $SIGNED_URL

then the upload works fine (so there's not an issue with the signed urls). I've also set the referer to various things with curl and it still works, so I don't think there is a CORS issue either. I'm trying to upload a file blob using javascript as follows:

var xmlhttp = new XMLHttpRequest();    
xmlhttp.open("PUT", $SIGNED_URL);
xmlhttp.setRequestHeader('Content-Type', blob.type);
xmlhttp.send(blob);

This always returns a 403 Forbidden error. I'm finding it surprisingly difficult to find any information online about PUTing data to S3 from javascript. I realize now that it's more common to POST form data, but is there any way to modify what I'm doing to also work?