If your spouses visa is expired, will they get deported while awaiting paperwork for a greencard?

If you are a US citizen and your foreign national spouse are already  married and have submitted the petitions for her permanent residence (I-130 and I-485), even if she is now out of status because her I-94 is expired, as long as she entered the US lawfully and is in a bona fide marriage with a US citizen AND the applications have been submitted, she will not be removed from the US.  YOu need to provide more information, however, as to the specific situation your wife is in, in terms of her initial entry to the US, and whether and when you have submitted the paperwork for her adjustment of status to permanenat residence on the basis of marriage.