There will likely be a compromise of sorts - Strikers can't go on for ever but they won't lose their jobs. The govt will fudge it - but there'll be concessions. There'll be much face-saving.
Then the likely response will be future - proofing. Just as they did with energy, miners, car production, printing, dockers. Outsource, relocate, privatise, modernise. That way the economy can get moving again - and the government protects itself from being held to ransom.
If you remember previous periods - what happened then? The govt gave in if they had to - but then dismantled the industry. It took years for people to recover from the damage, (small businesses, satellite businesses, individuals, families, towns, whole industries).
It did lead to social change though - not always in the way people expected - but it did. And some of it was for the better - although some of it possibly wasn't. A matter of opinion.
There isn't as much support as people think - but again it's not something people like to say because it's not "cool". So they'll say "Yay we support the NHS" and beep their horn and bathe in the approval of their mates. But they are fucking furious and frightened when yet again their hospital appointment is cancelled or it costs them £60 in cabs to get to work where they earn £75. (And if they don't go in sooner or later they'll lose the job anyway).
So that's how I think it will end. But I don't know any better than anyone else.