Change the -1 mtime option to adjust the modified date. -2 will be two days ago, -3 three days, etc... You'll want to do a fullbackup and
Putting the backup directory under /home/user creates a problem with the find. It's best not to put it there.
for i in `find /home/user -type f -mtime -1`; do
mkdir -p $DEST
cp -a $i $DEST
You may want to look at rsync using the timestamp options, even for local copies. It will be a bit more robust.