Of course you're running late.
Let me guess - you're a young pup. It's always been the same, since the dawn of history. Every generation laments that succceeding generation has to make the same mistakes, and learn the same lessons, over and over again.
IBM solved this estimation problem back when dinosaurs roamed the earth, virtually all computers were made by IBM, and they came with a "free" (as in beer) systems engineer.
IBM's solution was that every level of management that had to review an engieer's estimate would triple the estimate of the person who reported to (almost invariably) him. So, if the estimate required two levels of managerial approval, the quote to the client was 9 times what the engineers figured it should be. If three levels of approval were needed, the official estimate was 27 times what the engineers came up with. Now you know how IBM was able to afford that "free" systems engineer with every computer.
Actually, there are ways to drasticly increase the likelihood of success on "mission impossible" projects. I successfully led an EDI implementation project where there was no spec, no data, no customer, no access to the computers, the programming had to be done in an obscure language, and there was an arbitrarily set deadline of three weeks. Sometimes you take on such projects because you want to stretch yourself. But that's a story for another day.