Lucky you! My experience in doing genealogical research has been if you had ancestors in the original 13 colonies before 1680, chances are pretty good that you are related.
The reasons are simple:
- The relatively small pool of people (and subsequently, available marriage partners).
- The fact that even among that small pool of people there were many relatives from the same pool of English settlers (the "Children of Cromwell" effect).
- The commonality in purpose which caused them to come to America in the first place also caused them to merge the various differing groups through marriage, usually within the first century or so. One such example (also in my own line) is the Dutch which settled New Amsterdam marrying with the Connecticut puritans who moved out of Massachusetts to practice a less strict version of Puritanism.
The close blood relationships between early settlers tend to fall apart after about 1680 because at that time the British rulers begin to greatly increase the pool of colonists through forced emigration for various reasons ranging from petty criminals to people hopelessly in debt and those simply deemed undesirable to remain behind.
Bottom line is that even if you don't share common ancestors with Obama through direct blood lineage, you most likely are still a distant cousin through marital relationships of your indirect lines.