I think it completely depends on the state. Call around to the places you need to deal with (Marriage license place, whatever it may be called in your state, DMV/BMV, and the SS office).
Here in Indiana, it was actually really simple and I got everything done in 3 days over my lunch breaks. Our marriage license was ready for me to pick up when we got back from our honeymoon (1 week), some states mail your license back to you and others make you come in and pick it up. The next day I went to the SS office and it took all of 2 minutes once I got up to the clerk, to get my receipt for proof of my name change. Make sure you fill out the form before you go in, it'll make it easier. The next day, I went to the BMV to change my drivers license. All they wanted was my old license, proof of my address change, my SS receipt and a certified copy of my marriage license. I got my new SS card about 2 weeks after i applied for it.
I saw you were getting married in one state but live in another, which might take longer to get a certified copy of your marriage license. Call the county in which you are getting married and ask how you can get a copy of the license after the wedding, see if they mail it or if you physically have to go in to pick it up (or if someone else can come pick it up for you).
Personally, I'd probably go the safe route and wait until after you travel to get it done just incase something messed up the process.