Check what the school that you are mainly interested in says about this. For example Harvard has clearly said that if you apply late you will get the decision later but your changes of getting in are the same.
And that's the worry @licknee10 -- I'd love to aim for those very schools! Harvard updated their policy to include acceptance of the highest scores. But other policies are more ambiguous.
@kendallM Harvard is again ranked at #2 ... now). I do not see Harvard tightening their admission standards so ... Yale (or at least tie). Harvard has very large class sizes ...
... middle of the class at Harvard. Honors and law review are ... /cdoprospectivestudents2014employstats.htm Harvard
https://hls.harvard.edu/content/uploads/2015 ...
Quite the understatement. Harvard/Yale/Stanford don't do merit-aid scholarships so you would have to be super poor to get some financial aid and even then isn't likely to be a full-ride.