This has to be about the biggest problem in workplaces all over the country, and in every sector: trying to do more (or at least the same) with less. Just look at the poor sods at the Environment Agency, vilified by government for having cut back flood defence activities, when the same government has decimated the resources they had to work with. Sorry, bit of a tangent there...
Anyway, the advice from vase is spot on. Spend some time, even on your day off (I don't generally advise that, but if it's to alleviate serious stress, it can be worth thinking about work on a day off) itemising all the jobs on your TO DO list:where are the deadlines, and how many man-hours will it take to do them? What source will you have at your disposal (be completely realistic... You aren't aiming to impress our boss with pie-in-the-sky projections of how brilliant your team will be.) Then on Monday, you pin down your line manager, and if he/she hasn't got time, let her know that you'll take it to her boss instead, and ask them straight out "I can do X% of my current workload... Which tasks do you want me to do, and which am I going to have to drop?"
That might sound a bit bald, but that is what it will come to either way, and you should not allow them to pass the buck your way. If a company has miscalculated what it can deliver, the responsibility for the mistake falls to the people who get paid extra to take that stress, and the people with the authority to recruit new staff, and the people who decided to lay off all those staff in the first place. We've all had to tighten our belts and go a bit further for our salaries the last few years, and mostly with good grace, but we don't have infinite capacity to do more and more and more with the same resource or less. Your job should not reduce you to tears, and you should not be routinely working hours you're not paid for... It will make you ill.