Is there anyway to mount a webpage?

You can't mount a http/https server as a filesystem since it won't provide a directory table for you. (I left a comment on why httpfs isn't what you need)

The best way to do the task is to make a list of the URLs you need to check and use a shell script (run from Automator for convenience perhaps?)

You will need to USE curl or wget which will do the http downloading for you (they both provide post and http basic auth support for sending login info, however you probably need to install them on Mac Os X, off the top of my head I've forgotten.)

You can get fancy and use diff to check automatically for changes in the files, so that you only need to get personally involved with the process when you really have to.

Need more info, I'll happily expand on this.

References:

• Wget and Curl
• Diff