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As methyl mentioned, there are 2 spaces between the month and the day, hence my request to use code tags.

Try this:
todays_date=`tail -1 /var/adm/messages|awk '{print $1 FS FS $2}'`
grep...

Can you post the output of:
tail -1 /var/adm/messages

Please use code tags.

Quote the variable:
grep "$todays_date" /var/adm/messages > syslog.`date +%d%m%y`.log