As Counterparty is a system that sits on top of an existing blockchain implementation, one of our distinct advantages is our ability to work on virtually any blockchain implementation. We work with Bitcoin today because it is the most proven, most secure, and most popular implementation out there. However, if Bitcoin had serious issues in the future, we could move to a different blockchain (and/or support multiple blockchains, if necessary). This makes us not tied to the rise and potential fall of any blockchain implementation in particular, and is a major selling point of Counterparty.
Realistically, the act of switching blockchains would be a bit disruptive overall. Upon achieving overwhelming community support and approval for the switch, we would basically implement the code to support the new blockchain, perform extensive testing (involving the community deeply), and set a date for the transition, allowing people to prepare. At that transition date, we would then freeze balances at a certain point, and then begin production operations on the new chain. Existing XCP holders would maintain their exact same holdings on the new chain, and things would continue as normal to the maximum extent possible.