When Parliament gets its vote, the two year exit period will almost certainly be almost over and a vote of Parliament will not be able to stop the exit. Instead it will be a vote on the new arrangements with the EU. So either they just have to rubberstamp whatever gets put to them or - if they vote down these new arrangements - Britain will be left outside of the EU without any new deal in place.
So possibly, but there is talk of Teresa May rewording the Bill and forcing it through. Democracy eh!
Just like Trump and the electoral college, if we project the vote into MP constituencies Brexit got 60% [0].
This means that most MPs voting 'No' to Brexit would anger their constituents for Subverting Democracy - one of Theresa May's favorite talking points[1]. This would likely lead to a more extreme/populist government in the next election, and perhaps some internal strife and riots in the meantime.
Who would you rather have at the helm?
[0] http://www.businessinsider.com/nomura-2-charts-show-why-rema... [1] https://www.google.com/search?q=subverting+democracy