May is negotiating with the Commons, not the EU

It has long been obvious that "no deal" is a bigger threat to the UK economy than to the EU's. Mrs May is not taking "no deal" off the table because she feels it is her strongest weapon in her fight to get the Commons to ratify the May-Barnier withdrawal contract. (A reminder: half of UK's trade is with the EU; less than a fifth of the EU's trade is with the UK.)  For an analysis of what possibilities remain, see this.

Similarly, EU27 citizens living in the UK may not be bargaining chips in the Brussels poker game, as the government has pledged they would not be, but they clearly are when it comes to forcing her deal through Parliament, as Mrs May confirmed yesterday at prime minister's question time:

Ian Blackford (Ross, Skye and Lochaber) (SNP) Tove Macdonald is 87 years old. She was brought up under Nazi occupation in Denmark. She has lived in Scotland for 59 years. Why, Prime Minister, is she being forced to register in a country she has called home for almost the last 60 years?

The Prime Minister We want to ensure that EU citizens who are living here have their rights protected. We want to be able to ensure that they have the necessary support that they need and, indeed, the recognition of their status here in the United Kingdom. If the right hon. Gentleman is interested in defending and protecting the rights of EU citizens here in this country, then I hope he will vote for the deal, which does exactly that.

My emphasis.