Membership plug-in SAML 2.0 compliant
It could definitely be done with custom programming and it looks like there are a number of PHP libraries available that implement it: https://www.google.ca/search?q=php+SAML
We've implemented other custom login systems before that piggyback on another system, a rough guesstimate would be 10-20 hours of custom programming and testing.
I'd ask a lot of questions about what they're really trying to accomplish. And how long is it going to take to offset the cost of setting up SSO across all their applications as measured against time saved, etc?
The simplest solution would be just to setup a .htaccess file to password protect the folders, or website membership.
Hope that helps, I've built lots of intranets, let me know if I can be of any assistance in answering questions.