Currently (November 2009), the Windows Azure Tools for Visual Studio only support Web Application projects – the type of Web projects that have a project file and are compiled.
For most folks, they reason to choose a Web Site project was for the ability to update it easily on the server and generally, the target customer for Windows Azure is typically using a Web Application project. (for a good article about the differences and when to use each one, please see this post)
Because Windows Azure has a deployment model where you can’t update the files on the server itself and considering the target customer, this seemed like a reasonable approach.
That said, there are a lot of apps out there that are in the Web Site format that folks want to deploy to Windows Azure and we’re figuring out the best way to support this moving forward.
For the time being, most folks are doing the conversion from Web Site to Web Application project and I wanted to point to a good post off the Visual Web Developer blog that will help make this easier: http://blogs.msdn.com/webdevtools/archive/2009/10/29/converting-a-web-site-project-to-a-web-application-project.aspx