No, it's a bad idea. You could take this money out, but it's a very bad idea, because you'd have to report this income. If this is truly SSI, it is strictly income based. If it can't start till you lose your unemployment, then it very likely is SSI, and income based, not Social Security Disability payments, which are not. When you apply to SSI, they take your income very regularly and recertify and decertify quite regularly. so you'd have to report the IRA money if you got it out, else be in trouble for fraud, and it would probably be enough income to alter her eligibility significantly for a long period of time, even though it's going to be much less than it would be if you waited till you were 59 and a half, and even though you spent it immediately.
You're trying to overplan, thinking how you'd make it if you don't find another job and had to try to live on just your wife's SSI which is somewhere around $650 a month. But taking the IRA early will really hurt you as far as how much of it you get. "Substantial penalties for early withdrawal" makes it something you should only consider if you are absolutely about to lose the house, and this hasn't happened yet.
I am very experienced with working with people who lose long term jobs like this. The first thing you tend to do in your thinking and planning is "catastrophize," think what will happen if you never ever find another job and have to lose everything you've got and starve and freeze in the dark. But it is very likely you'll find something else, even if it's not as good as what you have had for so long.
Having a house payment would be okay when you do get another job, just hang on till then as best you can. About the worst things you can do for yourself when you are trying to get on any sort of income based program is pay off your debts. Sadly, then you have no expenses to count against the income you have coming in, and it decreases your likelihood of qualifying for the program.
Just keep looking for another job and work forward from that. Good luck to you.