CentOS is notorious for using yum as its package manager (the equivalent of Ubuntu's 'apt-get'). Yum is dependent on the Python version that ships with CentOS, so upgrading to python 2.7 simply kills yum and breaks the system updates. Here's how to solve this.
Long story short: You can follow the instructions here:
https://github.com/h2oai/h2o-2/wiki/Installing-python-2.7-on-centos-6.3.-Follow-this-sequence-exactly-for-centos-machine-only
Or simply use my gist based on this post and my previous post:
https://gist.githubusercontent.com/guy4261/0e9f4081f1c6b078b436/raw/bfded5dd1c53284a83872bc61444511e02d99212/python2.7.9_centos_installation.sh
