"RESOLVE REQUESTING THE SENATORS AND REPRESENTATIVES IN CONGRESS TO PROPOSE AN AMENDMENT TO THE CONSTITUTION PROVIDING, THAT NONE BUT NATURAL BORN SUBJECTS BE ELIGIBLE TO CERTAIN OFFICES."
"...That (in addition to the other qualifications prescribed by said Constitution) no person shall be eligible as President or Vice President of ye United States nor shall any person be a Senator or Representative in ye Congress of ye United States except a natural born Citizen ; or unless he shall have been a Resident in the United States at ye time of ye declaration of Independence, and shall have continued either to reside within the same, or to be employed in, its service from that period to ye time of his election."
A similar proposal for senators was made during the Constitutional Convention but voted down after James Wilson objected. He argued that he was helping to draft the constitution but under the same document he would be prohibited from serving in its government (he was born in Scotland). I suspect that was the main reason for the grandfather clause.
They hadn't yet got the message. :)