The other answers will work for most strings, but you can end up unescaping an already escaped double quote, which is probably not what you want.
To work correctly, you are going to need to escape all backslashes and then escape all double quotes, like this:
var test_str = '"first \\" middle \\" last "';
var result = test_str.replace(/\\/g, '\\\\').replace(/\"/g, '\\"');
depending on how you need to use the string, and the other escaped charaters involved, this may still have some issues, but I think it will probably work in most cases.