First, I am in CA. I was recently granted exclusive use of the home and effective July 15th I am responsible for all household expenses. The mortgage is in my husbands name and there was a grant deed adding me to the house last May. Must I actually pay the mortgage though? It's $2700/month with tax and ins. I have been a stay-at-home mom for 5 years now and assuming he pays child and spousal support it will leave me just $900/month for all other expenses... we have three kids together and I have another who lives just with me, dad doesn't pay support.

California is a "community property" state, which means that many assets and obligations of one partner created in a marriage become "community" assets or obligations.
The Family Home in a California Divorce | divorcenet.com (http://www.divorcenet.com/states/california/the_family_home_in_a_ca_divorce)

This would be spelled in in the separation or divorce decree.

... Must I actually pay the mortgage though? ...

If it's not said in the decree, perhaps not. And if you did not sign the mortgage note, you would not be responsible for any deficiency. But if someone doesn't pay, the holder of the note will foreclose.

And if your ex is sued for a deficiency, I expect he may come after you, either by asking to amend the decree or an independent lawsuit.

If your ex had an attorney, he or she might want to be sure the malpractice insurance was paid.

I think the term "all household expenses" is the fuzzy term here, to me, it would mean any and all bills associated with the house" I am not up on California case law that may or may not have defined it though prior court action.

But I would say unless he was ordered to pay it ( but even if he was ordered to, he may stop anyway) you should have considered in the request how you were going to pay for it)