Think of this problem as you need to give one NAME for internet users. As we all agree you can't give one IP as this limits availability and is at the mercy of your circuit availability. By changing focus the issue then becomes how do you resolve that name and what IP will it resolve to? This changes the scope of the problem and gives you some options.
If you can do this by name (which is the optimum way) you are going to need to implement a global load balancing solution and you are going to want to be in a position where you can manage your DNS. In essence the problem is how the client is configured to access your application. You definitely can't do this if you are trying to access services by IP address only. If this is a requirement then it is a done deal and you are going to have to continue to work with what you have.
If you are in fact stuck with using IP addresses then you can revert to a simple solution using a hosts file on the machines in question. Windows (assuming they are using Windows) will resolve a name using the hosts file before it tries to contact a nameserver. If you try to access www.example.com and you have two entries in the hosts file it will try each of these in succession until one works. If you don't have alot of end-users affected by your problem you are presenting this is probably the easiest and cheapest way to go about this. You can also load balance users across the two circuits by alternating the ordering of the addresses in the hosts file.
On the other hand with a GSS (or any global load balancing solution for that matter) being authoritative for your namespace you will be able to put in place the mechanisms you need to affect how the name for your service is resolved. The GSS device or devices do not have to be offsite. They just have to be able to get out through your internet connections. Once you introducde any global load balancing solution into the architecture you increase by orders of magnitude the way you can affect traffic reaching your server. This will be helpful in instances of circuit maintenance, equipment maintenance, physical relocation, introducing new servers, redirecting users based on geographic location, etc.
Just make sure you consider the scope of your problem as you are starting to move up to a more advanced solution and it will take some planning and some money. Not sure how many users you are talking about. If it is a small number then a host file modification will do the trick. You do not even need to add a legitimate domain to the hosts file to make this work either as Windows is just going resolve the name to whatever addresses you have configured.
ALSO - please be mindful of all of the additional info Jon and Paolo have provided. In the end this may be too much to tackle so take it offsite to a cheap hosted solution and save yourself alot of trouble.
AND - my public apologies to Paolo! I do not mean any disrespect as this discussion has become lively to say the least and I was probably a bit too blunt due to major lack of sleep.
Shawn
