Incredibly bad idea. Not so much the abillity to restore the Internet, which might become an issue if it's dropped defensively by some kind of "kill switches" used by various nations during a global conflict just as easily as by terrorists, but simply in the choice of who is holding those key cards.
I understand the political situation, and why they are going that multi-national for trust related reasons, but if this is serious there is no way some nations like "China" should have a card holder. The Internet is about free speech and sharing information, nations that have draconian limitations on free speech and/or have been engaging in "national firewall" type programs to filter information should not be involved in this at all.
Some of those nations having key cards seems like a natural invitation for them to intentionally NOT reboot the system if there was a massive incident, which would play more to their attitudes and philosophy than recovering it. Not to mention me wondering if this is true (and it sounds kind of hokey despite everything), because depending on how much data is on those cards it also means that doing a reboot someone could effectively tamper with the entire fabric of the Internet. A nation causing an incident specifically so they could see their card used in order to change things for example.
As odd as it sounds I would say that full sets of cards should be in the hands of the US and Britan to act exclusively as the first choices for a reset. International card holders should only come into play if for some reason all the other ones were neutralized.
Terrorism aside, if a serious war was to break out neither side given the likely divide would be able to put together enough cards. That might be part of the whole idea, but at the same time that's inherantly stupid since the bottom line is to be able to bring the internet back up as I understand it.