You should be able to choose the default wordsize at compilation time, generally by using one of the -m32 or -m64 options.
/usr/include/i386-linux-gnu/bits/wordsize.h is designed to be used when compiling 32 bit applications.
There should be a /usr/include/x86_64-linux-gnu/bits/wordsize.h containing a 64 bit __WORDSIZE definition.
This change was introduced with Ubuntu 11.4: https://wiki.ubuntu.com/MultiarchSpec
If -m64 fails, you might have a 32 bit distribution. uname -m will tell you.
Although it is possible to cross compile 64 bit binaries on a 32 bit system, that would be inconvenient as you won't have any simple way to run them there.
If your CPU is a 64 bit model (check with lscpu), you might want to install a 64 bit distribution to be able to easily build multiarch packages.