apt-get update fails (oom killer executed on /usr/lib/apt/methods/https memory hog)

I am repeatedly seeing the apt-get update/install process leading to a situation in which /usr/lib/apt/methods/https eats up the system's memory and as a result the OS oom killer is triggered. The OOM killer kills off the https process and the apt-get operation fails.

I'm running on EC2 t2.smalls and t2.mediums.

$ lsb_release -a
No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 14.04.2 LTS
Release:    14.04
Codename:   trusty
$ uname -a
Linux stage-app1 3.13.0-48-generic #80-Ubuntu SMP Thu Mar 12 11:16:15 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux