I don't know what those Democrats were thinking. Do they honestly think voting for it would've been a strike against their reelection chances?
In Barrow's case, yes. His district will remain a GOP target for probably as long as he holds it. Also, $7.25 to $10.10 is a rather steep increase in the minimum wage. A more modest increase, in the range of $8 to $9 would gain more votes, tho probably not enough to pass in the current House.
That seat will be a GOP target no matter what, of course, but do you really think they would use this vote as an attack? I bet they have plenty of other things to use against him. Like him ever being within 3 feet of Obama.