In the Debian philosophy of things, the package itself only contains what you need to run the things that need it, not compile. For most cases this is great, since you don't have to download and install stuff you don't actually need.
For compiling you need the package-dev, which should be something akin to libcurl-dev in this case. Do an apt-cache search curl to find out yourself.
Also as an additional hint, for installing one should probably use aptitude instead of apt-get for better dependency solving and less problems.