I'm not sure I'd worry eitherway, we got served a completion notice for 2 July, however the house was not completed until nearly two weeks later, we then had to complete snag list, order final valuation etc. and it was almost 4 weeks later when we finally completed.
I know its a new house situation, and I'm not sure yours is, but I believe that sometimes the solicitors of vendors include a competion date that is not realistic. Get your own solicitor to contact them and inform them that you want the completion date later than that.