Just leave. These people are screwing you and you were stupid not yo have discussed these things before accepting job. In future, use your brain.

Benefits are negotiated and not automatic. That includes paid holidays and vacation. This is especially important for nanny jobs since they often have benefits but are still hourly jobs and most MBs will likely assume (before they know about nanny norms) that an hourly job is not one that comes with benefits since most do not.

Tell them you misunderstood at the outset that they did not plan to include benefits but that this is a deal breaker for you. Be prepared that they may say it is a deal breaker for them too though. It is very hard when one side wants to negotiate after the other believes the deal has been struck.

I always go into a job with my own contract if one isn't provided when they offically hire me. If I don't receive one at before my start date I hand them mine. I give them a week to look it over, if they don't sign it or refuse, I start looking for a new position. I leave the position as soon as I get a new one unless I have enough in savings. I do mention it over again before I terminate the position.

Honestly, the best bet is to have them agree to your contract before your starting day. The day before you start you get the signed contract and on your first day you get car seat and keys to their house.

Today was not a holiday for the vast majority of people. Benefits are not obligatory.

Most nannies are working today without additional pay. It isn't a holiday for most of us.
Your problem is that you did not get a contract before you took the job. Your MB does not "need" to offer you any benefits. As the pp mentioned, you cannot assume people know these things. You said you told the family when your vacation was, but was paid vacation part of your package?
This is why this all needs to be put in writing before you start the job. That way, if there are any problems, you refer back to the contract.
A red flag for you should have been that they did not want to do a contract. It sounds like you are not going to change this family at all. Take this as a learning experience. Get everything in writing up front and do not start working for a family until you have a signed contract.

You can't just assume people know things. When you weren't paid for the week at Christmas, you should have asked about it. "I noticed I wasn't paid for the week of Christmas. I'm sorry for the confusion, but when I talked about taking a week at Christmas and a week in the summer, I meant for those to be my two weeks of paid vacation."

http://www.care.com/child-care-sample-nanny-contract-p1017-q33455259.html

I took the job thinking everything was on board. The family seemed to know about nannies seemed to have done their research etc. took the job asked about the contract they didn't want to do one. My husband says to talk with them once more before I leave. I feel like I work for absolutely nothing. I told the family I take my vacation the week of Christmas and 1 week in summer, that was fine but of course I did not get any pay Christmas week. I'm thinking what I need is a website outling a contract, vacation days etc to actually show them.

Why did you take this job? Are you paid under the table?

How to bring up to my MB that she needs to offer some type of benefits? She doesn't want to do a contract, I'm working today without additional pay and I don't think my mb understands? How to talk to her before I leave?