In the Compatibility Definition Document, Google has actually outlined the minimum specs needed for Daydream VR-ready smartphones. Among many other things. The CDD was actually created by Google to have requirements for their partners Android devices. So you'll see things that pertain to software and hardware in here. Google hasn't made the requirements for Daydream public, but thanks to the CDD we do know the majority of the requirements needed.
The biggest requirement, which is a bit of a surprise, is the fact that it must have a resolution of at least 1080p (that's 1920×1080). A bit surprising because VR is much, much better with QHD. However, the Pixel is a FHD display, instead of QHD, so it's not that big of a surprise. Google does still "strongly recommend" a display of 2560×1440 resolution or higher. Other requirements outlined in the CDD include having at least two physical cores, support sustained performance mode, support Vulkan Hardware Level 9 and it "should" also support Vulkan Hardware Level 1. It's strongly recommended that the device supports android.hardware.sensor.hifi_sensors and it must meet the gyroscope, accelerometer and magnetometer related requirements for android.hardware.hifi_sensors. Google wants the display to measure between 4.7-inches and 6-inches, which means no tablets. It also must support at least 60Hz while in VR mode. Also, in regards to the display, Google wants the display latency on Gray-to-Gray, White-to-Black and Black-t0-White switching time to be less than or equal to 3 ms.
So Google is pretty picky about what they want out of Daydream VR-ready smartphones and they definitely should. Seeing as Daydream VR is a step above what Cardboard was, Google wants to be sure that no matter what device users are using with Daydream, that they have a great experience. Daydream VR is likely going to be the best virtual reality experience you can get without picking up the HTC Vive or Oculus Rift, which will cost much more money, as expected. You can check out the full Compatibility Definition Document using the link down below. There's plenty of information about what Google requires from their partners in their smartphones, tablets and other products running Android.