Yesterday it was the EU that was defeated as much as was Mrs May, for it was their joint deal that failed. Now that a vote of no confidence in her government has failed she is in a position to tell the EU that if they want to avoid the prospect of a no-deal Brexit they must be prepared to re-open substantial negotiations. If they do not they face being blamed should that occur.
Once she has consulted MPs from various groupings she will be in an even stronger position to push the EU to move towards a deal which will command the respect of Parliament. If they do not then they will push her towards no-deal