Since taking office last year, Gov. Andrew M. Cuomo has done many things well, positioning himself for a possible presidential run.

He has challenged — and outmaneuvered — Albany’s wily Legislature. He has kept his once-notorious temper from spilling over. He has built a prodigious fund-raising operation and earned poll numbers that are the envy of governors nationwide.

But now Mr. Cuomo, a man who likes to determine his own destiny, faces a variable beyond his control: Hillary Rodham Clinton.

Creating frustration for his inner circle, as Mr. Cuomo considers a 2016 campaign for the White House, the eyes of his party are fixed on Mrs. Clinton, whose already sky-high stature among Democratic activists was enhanced by her husband’s crowd-pleasing speech this month at the party’s convention in Charlotte, N.C., and who can count on broad support if she decides to run.