No, you can't. But you can set it to a very high value like 100 years (about 3.000.000.000 seconds).
Alternatively you could abandon the build-in TTL index mechanism and replicate the functionality on the client-side. MongoDBs TTL is quite primitive. All it does is call db.collection.remove({date:{$lt: new Date() - ttl })
at regular intervals. Replicating this on the application-side is often not really much work.