Well first a few thing to check for.
1. Nexthop for internet is reachable via VRF or Global?
2. Do we already have NAT configured which is VRF aware, since you talk about private addressing, NAT is necessary.
3. If internet nexthop is reachable via global add a static route as mentioned in the document.
ip route vrf customer1 0.0.0.0 0.0.0.0 192.168.67.1 global
Now make sure that you are able to ping 4.2.2.2 from VRF.
For vrf aware NAT refer to below document
http://www.cisco.com/en/US/docs/ios/12_3t/12_3t14/feature/guide/gtnatvi.html
I hope you find this useful. Please rate the helpfulness of this document.
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Regards,
Sebastian Fernandez