I doubt there are any backdoors in RSA keys, but most https traffic uses 256-bit symmetric keys. Let's say the NSA or whoever has a bank of computers that can crack that key in a day. With today's CPUs, you could encrypt your traffic with 10,000 keys relatively quickly. Then they would have to decrypt each one at a time. Of course, exchanging those keys may be complicated. Maybe to accomplish that you need a 4096-bit key.
The biggest problem with this theory is if they can crack a key, how long does it take? 0.001 second, 1 second, 1 day, 1 year, etc? A 10,000 key deep encryption would be fine if it takes a day to break but obviously not if the process can be completed in 2 seconds.
I've really thought about starting a service that writes OTPs to a 2TB drive, sends them to customers, and they use that to connect back to offshore servers that act as a proxy for them. Then, unless someone tampered with the drives intransit all communications would be secure.