Referendum and undemocratic don’t belong in the same sentence. You’ve contradicted yourself. By definition, a second referendum cannot be undemocratic. Not holding one can be though, given that polls suggests the following; public rejects May’s deal, public favours Remain, and finally, is in favour of holding a second referendum. It’s undemocratic and ‘Stalinist’ (nod to Grendel) to not hold a second referendum.
As for a cross-party solution? Not happening, early in the process it may have been possible. Labour is risking electoral oblivion if it supports May’s deal. It’s suicide. On the flip side, there’s no downside for Labour to support a second referendum, despite many Labour strongholds voting Leave.
This sums up it up reasonably well.
Party activists pile pressure on Corbyn to back second vote