Among other things:
-- Presidents set goals and priorities. That's easily said, but hard to do. The natural temptation is to accumulate goals and priorities atop each other. (See Clinton, Bill, State of the Union addresses of.) But if everything is a priority, nothing is a priority. (See Clinton, Bill, presidency of.) To govern is to choose. To choose requires extreme mental discipline: This I do first, this I do second if I can, this must wait for third, these next 997 things probably don't get done at all.
-- Presidents align means with ends. Congress is the place where the American people register their wishes: Generous Medicare and Social Security benefits and low taxes; global military predominance but no casualties; perfect airline security with no personal inconvenience. It's the president's job to bring the system into balance, to set budgets, to force tradeoffs.
-- Presidents are deal-makers. There's a story told about Harry Truman in the last days of his presidency, awaiting the transition to Dwight Eisenhower after the election of 1952. Truman supposedly said to an aide, "Poor Ike. He'll sit at this desk. He'll say 'do this' and 'do that.' And nothing will happen! It won't be like the Army at all." The president cannot tell Congress what to do. He can't tell a governor what to do. He can't even safely tell the CIA what to do. (If they don't like it, they'll leak against him.) And that's even before we get to foreign governments. A president doesn't get what he wants. A president gets what he negotiates.
Maybe what Americans are hearkening for is the analytic ability and negotiating prowess of the former CEO of America's most successful management consulting firm. And just possibly, Republican primary voters have the self-control not to let the controversy over Romney's health care record cloud their respect for their front-runner's genuine executive abilities.