His stature and status in the eyes of the American people in addition to being one of a small handful of nationally recognized figures.

A little background: the Founding Fathers knew that what they and the country were attempting with republican government was an experiment especially concerning the peaceful transition of executive power. During the Constitutional Convention many delegates either wanted a 3-man executive council or to severely curtail the powers of the executive. What allowed these delegates to vote for the system as laid down in the Constitution was the assumption or knowledge that Washington would be the first president and thus able to hold the country together during it's most formative and vulnerable years.

There were some people, namely Alexander Hamilton, who believed that although Washington would win he would not win unanimously or would even be tied. Anything short of a unanimous win would embarrass Washington and a tie that would throw the election to the House would be an embarrassment to both Washington and the new Constitution. Hamilton thus maneuvered several votes away from John Adams, the man he thought could tie Washington, to other candidates. Washington ended up winning unanimously in the end anyways while Adams won nearly half the votes.

Source: Washington: A Life by Ron Chernow