In an example of how much of a threat eBay views Google's new payment system, eBay has altered their accepted payment policy to explicitly ban use of the new system. eBay does prohibit their users from using many other payment services that they view as rivals to PayPal, but do allow a select few. While it's plainly obvious as to why eBay would take such action, they cite other reasons such as Google Checkout not being old enough to be considered reliable:

Among the factors considered "is whether the payment service has a substantial historical track record," he said. "I won't say that's the only reason, but I will say that is a factor in evaluating payment services...Google Checkout is, what, a week old?! At this point we're saying it does not meet the factors needed to allow it as an accepted payment."
Google Checkout will likely never become an “accepted payment method” for eBay users. Seeing the rivalry between other Internet companies, this may be something that ends up in the courts.