Net install
Why not give the net installer a try?
excerpt
A network install or netinst CD is a single CD which enables you to install the entire operating system. This single CD contains just the minimal amount of software to start the installation and fetch the remaining packages over the Internet.
Up to 280 MB in size, this image contains the installer and a small set of packages which allows the installation of a (very) basic system.
There are several videos online that will walk you through how to do a netinstall, such as this one titled: "Debian 6.0 Squeeze - netinst - minimal installation". This video shows Squeeze (6.x) but it should be very similar to Wheezy (7.x).
Trimming your install
Also during the installation I would pick the minimal amount of packages in this dialog.

Expert installaiton
If either of these aren't sufficent to get into your 1GB limitation then you can always go with an expert installation and customize everything, down to the specific packages that get installed. Doing so it should be pretty easy to get under 1GB if you omit things like LibreOffice and GIMP. Here's a video that walks you through how to do this, titled: "Installing Debian Gnu/Linux Wheezy with Gnome 3". The video shows an installation using Sid, but you should be able to follow it using Wheezy as well.