score:6
It doesn't matter what you wrote on the form - what matters is what was put in your passport.
If you check the stamp you got at entry it will say how long you are allowed stay in the country. For example, a few weeks ago I entered Singapore intending to stay for 1 night, so I put either 1 or 2 days on the form (I don't recall which), however on my passport the stamp says :
PERMITTED TO STAY IN SINGAPORE FOR NINETY DAYS FOR SOCIAL VISIT ONLY FROM DATE SHOWN ABOVE.
Thus I could have extended my 1 night stay up to 90 days without any repercussions.
The one catch with this is that Singapore entry stamps have a habit of smudging when stamped, so you may not actually be able to read the text referenced above, but as an American citizen you can pretty much guarantee that you'll have a standard "visit pass" that is valid for 90 days from entry.