I'm going to suggest this:
-- Set target to the upcoming midnight
set target to (current date) + 1 * days
set time of target to 0
-- Get all the uncompleted reminders due before the target and return their count
tell application "Reminders"
set dueList to every reminder whose due date < target and completed is false
get length of dueList
end tell
This matches what you'l find in the Today smart list in that it collects all of the uncompleted reminders in all of the lists that have due dates within the current day. The two lines at the top use AppleScript's weird date arithmetic to set the target variable to the upcoming midnight.