Are you a Premium member ?
If NO, then the API is of no use to you.

If you're not a Premium member, then there is no need to login to your account.
I think if you do something like this:
Code: 
opener.open("http://www.google.com/recaptcha/api/challenge?k=6LdNWbsSAAAAAIMksu-X7f5VgYy8bZiiJzlP83Rl&ajax=1&cachestop="+str(random.random()))
random.random() is a random no., between 0 & 1
You'll get the captcha Image.