Log in to the Google Spreadshet API using ClientLogin and PHP / cURL

I use the ClientLogin method and cURL to enter the Google API. This works great, and I get a token for later use. Now I can request docs.google.com using

        $curl = curl_init();

        $headers = array(
            "Authorization: GoogleLogin auth=" . $auth,
            "GData-Version: 3.0",
        );

        curl_setopt($curl, CURLOPT_URL, "https://docs.google.com/feeds/default/private/full");
        curl_setopt($curl, CURLOPT_HTTPHEADER, $headers);
        curl_setopt($curl, CURLOPT_POST, false);
        curl_setopt($curl, CURLOPT_RETURNTRANSFER, 1);

        $response = curl_exec($curl);
        curl_close($curl);

This works fine, and I get a list of all the documents available in my google docs account. But if I try the same request on spreadsheets.google.com with the URL obtained from the api documentation :

https://spreadsheets.google.com/feeds/spreadsheets/private/full

I get error 401 saying that the used token is invalid. I use the same token and request in both cases. Do I need another google spreadsheet token?

Edit: This is how I request a token:

        $clientlogin_url = "https://www.google.com/accounts/ClientLogin";
        $clientlogin_post = array(
            "accountType" => "HOSTED_OR_GOOGLE",
            "Email" => "my email",
            "Passwd" => "my password",
            "service" => "writely",
            "source" => "my application name"
        );

        $curl = curl_init($clientlogin_url);

        curl_setopt($curl, CURLOPT_POST, true);
        curl_setopt($curl, CURLOPT_POSTFIELDS, $clientlogin_post);
        curl_setopt($curl, CURLOPT_HTTPAUTH, CURLAUTH_ANY);
        curl_setopt($curl, CURLOPT_SSL_VERIFYPEER, false);
        curl_setopt($curl, CURLOPT_RETURNTRANSFER, 1);

        $response = curl_exec($curl);

        preg_match("/Auth=([a-z0-9_-]+)/i", $response, $matches);
        $auth = $matches[1];
        curl_close($curl);