Heather,
From my experience and from what I have read on this site there is absolutely no way I would close the purchase of a new property without, at the very minimum, snagging it myself and ideally getting a professional to snag it.
Check your contract for purchase and / or consult your solicitor because if I remember the standard new build purchase agreement includes a clause that allows you have any substantial defects remedied prior to closing.
In my opinion your builder is trying to pull a fast one! And, any commitments to remedy defects post closing the sale, unless they are in writing, are worthless.
BTW who told you that you would not be allowed to snag ? - the builder, the estate agent, the site foreman or your solicitor?