May won’t do anything of the sort, as nobody would support her as PM in a National Government. She has achieved the unique position in our history of becoming an authoritarian dictator without even the support of a huge section of her own party. The only legitimate action she can take following defeat on Tuesday is to resign and call a General Election.
I do agree something has to be done about Article 50, but the EU won’t allow extension on any terms, we have to have specific grounds for thinking that a new deal can be negotiated. A General Election followed by a Labour government would mean this is possible, without the iniquitous red lines that May has strangled herself with.
Personally, I would rather Parliament votes through an amendment to revoke Article 50 unilaterally, which is a legally valid move. That would allow time for a General Election and/or a second referendum. If, after all the potential chaos and hardship of Brexit which we now know awaits us the people still want to leave, then Article 50 can be triggered again, but only after a new trading and political relationship has already been agreed, with a full Customs Union in place.