I'm not a web developer, so I can't offer a time estimate. But I do proposals.
I definitely would not back off of my original estimate. If you do, it will look like you were dishonest in your original estimate, just seeing what you could get from them. Their comment sounds to me like a tactic to try to manipulate you into lowering your price. (If they really could do it in house in 8 hours why are they even shopping it out?)
And one good tactic deserves another... people will often want something when they see it slipping away from them. So take yourself away and hopefully they will panic and try to keep you.
I would (very politely) say something like this:
Wow, eight hours is fantastic. If you can do it in-house in that amount of time then you definitely should do that. If you have any problems at all, or just decide you don't want the hassle, please don't hesitate to contact me. Your project looks interesting and I'd love to be involved. But as far as my estimation process is concerned, I have a lot of experience doing this type of development. I'm aware of the myriad important details that are required that take time. I was very careful analyzing your project and considered all the ways I could save time in my estimate.
(The "or just decide you don't want the hassle" part is to help them save face if they try it in house or hire someone cheap who doesn't work out and want to come crawling back to you.)
If you really do think you over-estimated and want to lower your price to get the project I would not lower the price without taking anything away, because again, it will make you look like you were just trying to gouge them and they won't trust you. But you could take away something that's non critical or that you weren't going to do anyhow. For example:
"Wow, 8 hours is amazing. There is no way I can compete with that, but if you really don't want to do it yourself and my estimate is over your budget, there are some non-essential parts of the project you may be able to do without. The documentation for maintaining your custom site was 15 hours. We could use XYZ frames instead of the super cool ABC ones and save 10 hours. Rather than CSS we could do BSS. It won't be such a BFD but that will save you 20 hours... (I know nothing about web design so I made all that up, but I'm sure you can come up with some items to "take away" from your estimate if you want to lower the price.)
If you do lower the price - be very careful. The type of client that tries to get you from 120 hours down to 8 is likely the type of client who will become a major nightmare if you let them. The more you give, the more they expect/want. And the cheaper they are, the needier they are with very unrealistic expectations. They want to get something for nothing from you. They are probably not the kind of client that wants a long term, win-win business relationship.