As a practical matter you won't need more MongoDB router instances until you have a LOT of servers (each doing a LOT of traffic). Assuming you get to that point though the problem is really a lot easier to solve than you think it is.
Expanding on what MrKurt said, what you would typically do is split your Tomcat servers into groups, and then configure each Tomcat server group with a set of MongoDB routers for failover.
So if you have 30 Tomcat servers you could split them into 3 Tomcat groups of 10.
Then set up a Mongo router for each group, and configure something like:
Tomcat Group 1 -> Mongo 1, Mongo 2, Mongo 3
Tomcat Group 2 -> Mongo 2, Mongo 3, Mongo 1
Tomcat Group 3 -> Mongo 3, Mongo 1, Mongo 2
Each Tomcat server group is pointing at a different Mongo router
So you're not beating up one single front-end with all your requests.
If the default Mongo router for a group fails you fail over to the next one
This is handled by the MongoDB connection driver.
Note the staggering of the failover chain as shown above. This prevents you from dumping excessive load onto any one server in a single-fault condition.
If you lose a single tomcat instance you're not "wasting" the Mongo router
You would have to lose all Tomcat instances in a group in order to have one of the Mongo routers go idle (and even then it's not "wasted": It's still redundant capacity in the event of a failure of another Mongo router instance.