Ask them if you will be receiving a 1099. Self-employed people receive 1099s instead of the W-form series. If you are receiving a W-2 then the following doesn't apply.
Self-employed people must pay all the regular taxes you are accustomed to - federal, state income taxes, social security, FICA, etc but they pay all these plus an additional tax. They have to pay self-employment tax
which is the employee's/employer's share of social security/FICA. Self-employment tax is roughly 15%.
Self-employed people should make estimated quarterly payments to the IRS. I'd recommend you see an accountant or other tax person about this. I'd also be surprised if this status is to your benefit and if a nurse working as you describe actually meets the IRS criteria
for being a self-employed worker. There are some employers who are making their workers self-employed 1099 status to shirk costs and shift them to their workers when they do not even meet the IRS criteria. I'd also guess you aren't covered by worker's comp if you are on a 1099 self-employed status. I sure wouldn't want to be doing the physical work in LTC and not be covered by worker's comp in the event something happened.