The present impasse will probably lead to Britain never leaving the union. Except for a hard core of about a fifth of Parliament, all the other legislators are adamantly opposed to Britain leaving the EU without a deal; and the Union, knowing this, has no reason to negotiate further.
But the legislators will not agree to the deal as negotiated, as they have now demonstrated. They want a second referendum, in the hope that the result of the first will be reversed. (And if it is, there will never be a third.)
An extension to Britain’s departure will be granted only if Britain has a concrete proposal to offer — and the only such offer it can make is to hold the second referendum.
This is, in essence, the European approach to democracy: If the voters get the answer wrong, either ignore the verdict or make them vote again until they get the answer right.