Maybe it's time for a staff meeting. You don't need to make it a nasty or an accusative one - I might be inclined to approach it as a planning meeting. Sit down with your staff, a breakdown of what needs doing, and a timetable that will get you to the deadline. Split the work out and make sure you've clearly said to each person 'this is your part of the project, this is your deadline and if you're not going to be able to meet it I need you to tell me in good time and explain to me what the problem is.' Then make them repeat back to you what they're going to do and when they're going to do it by. Make sure you give them scope to air any problems ('Here's your deadline, do you see any potential problems with your meeting it?') so that, if they come back later and say 'you overworked me' or 'I didn't understand' you can say 'I did ask you if your part was ok and you said yes.'
Make sure you keep notes of the meeting so you have backup if they don't follow through.
Check up on them from time to time. 'How are you getting on with... are you still on track for your dealine? If not why not and what can I do to help sort your problem out?'
Then, if they do it - great. Make sure you then go round and say 'well done, that project worked really well, I think we'll do the next project the same way.'
If they don't do it... yes it'll be a swine to get the project in on time. On the other hand, you also have a case (if you feel it's justified) to go to your boss, HR or to whoever handles staff discipline in your office and say 'I have a problem with these people, here's how I managed the project and they didn't do their work and didn't tell me they wern't going to make the deadline I set them, now the project is behind and it's a serious problem. Here's my backup to show that I managed the project well and gave them opportunities to come to me with problems.'
If one of them walks away from you - as their supervisor you are perfectly entitled to call them back and say 'never walk away from me like that again. I expect you to treat me with respect and courtesy, as I do you. If I catch you treating anybody in the office with such rudeness again I will report you for it. Now, let's go back to what I was asking you about...'
People like this have often got to be carefully managed - because if they don't think they'll be checked up on and held to account for their work, they won't do it because you're letting them get away with it. It's like disciplining naughty children - they've fallen into a bad habit but if you don't teach them there are consequences for that habit and you will routinely discipline for it, they have no motivation to change their ways. It may not make you popular, but if you want the work doing, it's the only way.