TSA is now experiencing an increase in resignations. Given low pay and lack of serious career potential, in a locale where there is decent work available, it is just as easy to jump ship to a better-paying job. Many Officers are military veterans and do not have the benefit of long-term employment to build up a rainy day fund.
FBI agents and others are much better paid and are less likely to find comparable work and less likely to give up a solid law enforcement retirement benefit.
Many contractors were issued stop work orders on the date of the shut down, so it is not a matter of when they bill; they were simply prohibited from incurring the obligation. Their employees, the people who are referred to as "contractors" but who are really employees of a contractor are in trouble because they are highly unlikely to ever be paid.
Contractors also have to pay their people to work, if authorized. Only the federal government can both require an individual to work and then not pay him. Contractors also have other payments they cannot escape, e.g. rent and equipment costs. Some of those contractors won't make it through this and, if they do, because unemployment premiums are based on claims (in part), those who have laid off their people will experience higher costs for the next 3-5 years if they survive.