Unfortunately it is a "butt-to-butt" connection, I think. What I'm trying to do will look like this:

The two ends of the copper wire will meet at approximately 45 degree angles. This is going to be an antenna, so there's virtually going to be no stress on the wire itself.
There does need be be an electrical connection between the two ends, which I think someone said the solder will provide. But again, do I really have to heat up the wire enough to melt solder directly? I bought the 40W iron from RadioShack and after holding it on the wire for like 10 minutes it still wouldn't get hot enough to melt the solder!
Thanks,
Nathan