No, Brexit MPs are saying 2 years because that's what the law says will happen. Both EU and UK law agree on this. As of one year from next week, the UK will no longer be a member of the EU. To reverse that - is technically possible, but it would take political and legal manoeuvrings that would amount to a constitutional amendment.
The whole argument is about what, exactly, "member of the EU" does and doesn't mean. That turns out to be a surprisingly complex question.
If you'd asked me two years ago, for instance, I would have said that all member states send representatives to the council of ministers and to EU summits. But the UK stopped doing that immediately after the referendum. So in that sense, it's already not a full member of the EU.
Other aspects of membership - being bound by EU laws, courts, common foreign policy, common fisheries policy, participation in EU budget etc. - all turn out to be negotiable. Again, not what I'd have said if you asked me pre-referendum. Who knew? We're in uncharted waters.
"Ceasing to be a member" is easy. "Defining what that means" is something else entirely.