use the -O (capital 'O') option to force output file to retain a static file name. wget will append a .1, .2, .3, etc to index.html if that file exists locally already -- this is normal behavior and you would have found that behavior at the command line also. prove it to yourself by running the command multiple times at the command line.
also why not use -o output.log instead of redirecting stdout to output.log?
so just to be clear, the command would look like
wget -t0 -O index.html -o output.log http://www.page.com