My solution is to have the script ask the user to enter his password and store the value in a variable to be used along with Expect. The script installs Expect if it's not installed and then the script does:
read -p "Please enter your password: " PASSWD
export PASSWD
username=$USER
export username
if [[ ! `sudo -l -U "$USER" 2>&1 | grep "ALL"` ]]; then
expect -c '
spawn "su -c \"cat <<EOF >> /etc/sudoers.d/$env(username)
$env(username) ALL=(ALL:ALL) ALL
$env(username) ALL=(ALL) NOPASSWD:ALL
EOF
\"
"
expect "Password:\r"
send $env(PASSWD)
interact
'
fi