Financial fall-back

I think I've realized what my emergency fund goal should be set at to avoid any financial fall-backs on debt repayments. Rather than the $1000 commonly recommended, or the $750 I had established, I think it needs to be (while I'm still in debt repayment mode) around $5000. Why?

The "emergency" situations I've had lately including my car breaking down piece by piece with the last straw being the heater completely breaking on my way to the hospital. I wouldn't have replaced it and just relied on taxis in weather below 10 C, but the husband equivalent insisted I replace it. He did have a point, and we do have a newborn. It was about $5000. It would have been about $3000 to repair it to drive-able conditions, but all would be band-aid solutions. I then was in the waiting limbo to ensure I qualified for maternity employment insurance, which thankfully I had saved an additional amount for but knew I might have had to use my emergency fund.

Even more recently, the kidlet had a doctor's exam, which lead to referrals. She is going to need a procedure for a very common problem now that is easy to handle but if left, could be troublesome. I've already paid $800 to the specialist, and it will be about another $2000 to finish. So, I'm back in the line of credit. I have my fingers crossed that I'll get a big tax refund check to cover this. But it really shouldn't be this way.

The foreseeable emergencies I can think of - pet needing medical care, my daughter seeing the specialist, car troubles, needing to pay taxes or the first month of daycare when I return are all well over $1000 (the normal "recommended" emergency fund number), but should all fall (hopefully) under $5000. Hopefully, a $5000 buffer would handle not just one but two emergencies happening close together until I can build a larger nest egg, longer term budgeting to include things like vechile replacement savings goals, and finalizing family planning (aka one more baby or call it complete).

My plan is to play it day-by-day for a bit thinking about my budget and how I am going to rearrange to pay off this new and upcoming debt. Then, should I get a refund to fullfil my line of credit back to zero, start my new $5000 emergency fund and budget (if I can) to get it completed before I return to work where again I'll reevaluate how I'm going to crush this debt monster.

What is your emergency fund at now? What was it while you were paying off debt? How did you decide? Did you rely on tax refunds or did you have to save to make sure you could pay your annual taxes?