I don't think Coinbase support provides a direct phone number.
You have a few other options for contacting though that has worked for me, especially their twitter person:
Community discussion forum:
https://community.coinbase.com/
Twitter:
https://twitter.com/coinbase
Facebook page:
https://www.facebook.com/Coinbase
Or, you could send them a letter:
Coinbase Customer Support
548 Market Street, #23008
San Francisco, CA 94104-5401
USA
Oh, I never thought of using twitter or facebook! I hardly get on twitter but will for this. Do I tweet them publicly or is there a pm on twitter? Thanks, this at least gives me more ways to reach them.