I had a similar problem to the feeds before I upgraded to 3.7.1. However, that was because I am behind a firewall. I fixed that by defining proxies in my wp-config.php.
I still have the problem with plugin updates though. Although everything updates manually, I get those errors. I am assuming that it is because of the new feature of 3.7.1 and related to proxy as well.
I will post again if I find any solution.
Good luck!