S.D.
This is my answer from a post about a month ago - I just updated it.
I had a tubal last year about a day & a half after my 2nd was born. I did not get an epidural for the delivery (though I wanted it, no time), so they did a spinal for the surgery. Took about 15min, then recovery time in the recovery room. They would have left the epidural in place for it if I'd had one for the delivery. I really havent' had any problems. I breastfed so I didn't get my period back for a year. I've only had 3 since then (DS is 16mo) and they were normal like they always were. Sometimes I do get sharp pains on one side or the other, but it may also be ovarian cysts as I have PCOS. No other side effects. Since you are pregnant now, it is easier for them to do it soon after delivery (or while there in there if you have a c-section) because they can get to the tubes easier. My recovery was pretty easy. I had surgical pain for about 3-4days (took percocet) and then it was just incision pain for about a week or so longer. My incision is at the bottom of my belly button, so it's not noticable. And she placed clamps on the tubes which I think is what they are doing now instead of tying them off something. And the downtime for a tubal is not that bad - I still did most things, just had to take it easy for a couple weeks which you'd do anyway after giving birth ;)
I know people talk about hormonal imbalances & issues with tubals, but couldn't Essure cause the same problems since it is essentially the same thing - blocking the tubes. Just a thought. I've still had no issues since having my tubal and no regrets about having it done.