I clicked on the "Sign In to Web Albums" and entered my gmail username and password and got log in failure message. The log in window returned immediately showing "Login failed - Please try again later". The error was thrown in less than a second which was ample reason for me to believe that that this is a problem at my end, not at gmail end.
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Searched the web and got the solution suggesting to install "openssl-devel" package on my laptop.
# yum install openssl-devel
Tried to sign in to the web album again, but unfortunately still getting the same error message.
Banged on my head for a couple of minutes and finally realized that Fedora 13 running on my laptop was x86_64 and picasa is a 32 bit application and I must install openssl-devel.i686.
# yum install openssl-devel.i686
I was really happy after that. Everything worked as expected and my engagement photos are now live on picasa.