That's a good question, and a reminder for me to look at this issue again. I'm at a small school as well with 3 staff. I have some ideas on how this might work. Here's what I'm thinking for my situation.
1. Figure out who should have the authority and access to post emergency messages. I think this should extend beyond just the web team. Usually the PR team will craft the message, and I think it makes sense if they have the ability to post directly in case I'm unavailable. Campus security as well.
2. The technical stuff. I think one of the easier ways to post a message is to use an RSS feed. Have an application that the authorized individuals can log into and add a message. Have the home page setup to read this RSS file and display whatever messages it contains. We don't have a CMS so I plan to write a small app to handle this.
3. Mobile access. The app should be easy to use on a mobile device in case no one can get to a computer.
There are all kinds of scenarios that we're thinking about, from minor inconveniences to an earthquake taking out the campus. Finding something that works in all these cases is quite a challenge.
I agree that there should be a larger team able to post emergency updates to the home page, and that team should be identified with the assistance of the College's emergency management team. Ultimately, the role (as I see it) should be the responsibility of the people who fill the "Public Information Officer" role in the emergency plan.
To add to Erik's thoughts:
4) Consider how the home page should look in an emergency in advance of the emergency. This is a core consideration whenever we undergo a redesign. You don't want to spend time in Dreamweaver designing the emergency home page when the core factor is speed (i.e. getting the emergency message out ASAP). Developing a tool that can "write in" the emergency message as needed is critical to avoiding the Web team as a single point of failure.
5) The home page message should be one part of a larger emergency communication strategy. You can see past discussions on this site about social media expectations of our students. You don't necessarily need to use every media for every type of emergency.
6) Work with IT to develop the outline of a plan to get an emergency Web site online in the event that you lose your main servers. In what priority is restoration of the Web vs. other services?
Also, if you are assigning others the ability to post some kind of emergency message, make sure they are trained and drilled at least twice a year, maybe more. Otherwise it is a sure bet they will forget how to use the system in a moment of stress.
I understand your pain as a one man shop. At one of our emergency communication meetings the question was raised as to what happens if I'm not here in an emergency. I explained how there is no backup to me. That ruffled some feathers, to say the least. That said, nothing has changed either.