miniboxer, I run Arch64 and had the same problem. Here's your fix:
Basically, if you look at your log files, you will notice the following error:
java.lang.UnsatisfiedLinkError: /tekkit/bin/natives/liblwjgl.so: /tekkit/bin/natives/liblwjgl.so: wrong ELF class: ELFCLASS32 (Possible cause: architecture word width mismatch)
To fix, open your ~/.minecraft/bin/natives folder and copy all the files in there. Place them in your ~/.techniclauncher/*game-of-choice*/bin/natives folder. Say yes to any overwrite requests and you should be good to go!
**EDIT**
A few notes. The above fix only works if you have a separate vanilla minecraft .jar that you play. If you don't have one, go grab it and make sure it plays fine. Then you should be able to follow the above fix.
If that *doesn't* work for you, then you need to download them. Follow instructions here:
http://www.minecraftwiki.net/wiki/Tutorials/Update_LWJGL
Another thing to watch out for is that when you launch the game, it will go to the gray screen for about 5-10 seconds. Then it will sit on the MOJANG splash for about 30 seconds. So just give it some time when you launch it!
And kingsocarso, you can make ANYTHING run in linux. Especially java applications. Java is designed to be cross-platform compatible, so if you have a .jar file you can get it to work. :-)