Thank you both for your responses!

Slavery was abolished a long time ago Your employment is at will, and my guess is any term defined in the contract is loosely worded or doesn't provide good definitions of termination at will.

Contact the county where you are employed (not where you live) and they should have people in the labor department who can advise, and/or refer you to pro-bono help (like law students) if you're short on cash. Generally, laws on employment like this are strongly in favor of the employee.

I have given them 3 weeks notice, and started the process of finding a replacement. I also have another job that I begin in 3 weeks, so the reference is not crucial. I go back to school in a year and will no longer be a nanny.

Nobody can answer this without seeing your contract. But generally, the only thing they could do is sue you for damages. They can't force you to stay, and they can't withhold wages you have already earned. In practice, they are never going to sue you. The real issue is them giving you a bad reference - that is what will really hurt you. Try negotiating with them to find out what their issue is - do they just need you to stay on for a few more weeks until they get new childcare? That would be the responsible thing for you to do as well. Be firm and let them know you are not going to stay, but that you will help them in the transition.

I recently gave notice at my nanny job, and my employers reacted very calmly at first, but are now trying to maintain that our contract was for a fixed-term and that I cannot leave without "cause", defined by our contact only as failure to remit payment for 2 weeks. My question is for anyone with knowledge of contract law. What defines a fixed-term contract? Is the wording "This contract shall be in effect from ____ to ____." strong enough to define a fixed-term contract without stating that only termination for cause is allowable?

Some more information:
My paycheck has been late 6 times in the past 10 months, but for a few days to a week each time, but not the 2 weeks defined in the contract.
My employers are consistently late without notice. Consistent meaning it is not uncommon for my boss to be late every day in a week.
The termination for cause section of the contract is not specific as to which party it applies to, so would consistent tardiness on their part also be a "for cause" termination? and late paychecks "nonperformance of agreed upon duties"?

Any advice is welcome. I just want to have the facts straight before I confront them on these claims. Thanks!