No.. there was a Google phone. The Google Phone is the Passion/Nexus. It was originally to be sold by Google and unlocked. Due to Verizon's rejection of it, they went GSM based. Google failed in its goal.
This is why the Nexus is not an HTC phone and will have no logos or characteristics of an HTC phone, yet being manufactured by HTC. HTC was simply a hired gun by Google to manufacture the phone. It will not have "Sense." This was the phone that Google claimed to be "the vision" of what they thought a device should be. (In other words, nothing more than their opinion just like HTC, Samsung, Motorola, etc.)
(Note: Right now, unless AT&T makes changes, the Nexus was only receiving EDGE speed data, not 3G. A serious limitation. This is why T-Mobile has gotten the order from Google to promote it like they did the G-1, etc. This was not the original plan by Google but they have been forced to save face and change marketing strategies.)