The much-quoted clause 2 of the article says (my emphasis):
... the Union shall negotiate and conclude an agreement with [the withdrawing] State, setting out the arrangements for its withdrawal, taking account of the framework for its future relationship with the Union.Nothing is impossible, but insiders seem to agree that arrangements for withdrawal, coupled with an agreement on a framework for the future, can be completed within two years, but any actual trade deals will take longer, which could mean the UK is unable to do deals with non-EU countries for some time.
On the quiet, the government acknowledges this. When the CBI asks not to be left looking over the cliff edge of a sudden change in relationships, May and Brexit minister David Davis will acknowledge that time might be needed to complete the implementation of the deal. The word "transition" sometimes passes their lips but always as if it's implementation of a deal already signed.
"No deal is better than a bad deal," May has said. But there's no time limit on trade negotiations. The Article 50 deadline applies only to agreement on things like money, ex-pats, membership of security, scientific and other organisations. "Crashing out on WTO terms" is nothing to do with that, unless we make such a mess of it that we leave the EU and have to negotiate a free trade agreement from outside, but May is telling us it is.
My worry is that the government is feeding the expectation that everything will be done and dusted by 2019. The more vociferous Brexiters don't see why it should take even that long, but if we stay "unfree" past that date there will be more than grumbles.
We're going to see a brief battle in Parliament this week over the possibility of a "meaningful" vote on whatever deals emerge, but Gina Miller is right. - we won't know for a year or more what options we will have and should fight for. We won't know for about the same time whether an Article 50 notification can be withdrawn or reversed. Today we're in a phony war, which May wants to keep phony as long as possible.
I don't know what Parliament might have to vote on in 2018-19. I do know that May will have to manage expectations very differently to avoid massive disappointment, backbench revolts and perhaps worse. Farage has warned of "public anger" at any "betrayal". Less calculating voices suggest taking to the streets. A prime minister who seems terrified of telling us anything definite about the future might give them an excuse to deliver.