I needed to use the HTTPRequest class that comes as a PECL extension to PHP. This was easier than I thought. If you followed my instructions for installing PHP with Homebrew, then installing the PECL extensions should be even easier. Here's how:
Open up the Terminal and do:
$ pecl list-all
just as a sanity check to make sure you have PECL installed from your Homebrew installation of PHP. You will see a list of all available PECL packages, and, potentially after some "Warnings" from bugs in the PEAR code, you'll notice that "pecl/pecl_http" is in the list.
Before you can install anything with pecl, you need autoconf. It helps to build in the environment with which we're working. Just do:
$ brew install autoconf
Then install your favorite PECL extension (in my case, pecl_http):
$ pecl install pecl_http
Then a whole bunch of code garbage will fly past the screen. In a minute or two, some config options will appear. Press "return" to accept the defaults in brackets. When it's finished, you'll know.
If you got a fatal error during install, try running under sudo. If you still get an error, wait a day or two and maybe they'll push a bug fix?
Then just restart your web service (I just reboot my computer) and you're done!