By MARK LANDLER

WASHINGTON — Her image has been plastered on banners in Tahrir Square, crossed out with a blood-red X or distorted and smeared with insults. She is too cozy with Egypt’s deposed pr

Anne W. Patterson, a press-shy career diplomat who has been American ambassador to Cairo since 2011, suddenly finds herself a target in a dangerous political upheaval, a symbol for angry young Egyptians of America’s meddlesome role in their country’s affairs.

With the Egyptian military ousting President Mohamed Morsi on Wednesday, Ms. Patterson will have to navigate a perilous course between Mr. Morsi’s opponents and his enraged Islamist supporters, both of whom have grievances with the United States.

That she has become such a lightning rod for American policy speaks to the legacy of American involvement in Egypt and to the comparatively low level of attention Egypt has received from the Obama administration since the ouster of Hosni Mubarak two and a half years ago — at least until this week’s turmoil.

As her bosses in Washington struggle to exert even modest influence over the events in Cairo, Ms. Patterson, 63, has been portrayed as a sinister force by pro- and antigovernment protesters alike: a defender of the status quo as well as a troublemaker who schemes with the opposition.

“She’s being lambasted because she’s the face of America,” said Vali Nasr, a former State Department official who worked with Ms. Patterson when she was ambassador to Pakistan. “But the fact that she’s being excoriated instead of the president only represents the fact that the rest of the American administration is absent.”

In his first reaction to Mr. Morsi’s ouster, Mr. Obama warned of the dangers of violence and tried to steer Egypt’s military toward a prompt resumption of democratic rule. But the flurry of White House meetings and phone calls on Wednesday served to underscore the lack of leverage the United States has over Egypt, once a crucial strategic ally in the Middle East but lately just another headache.

Ms. Patterson’s problems started on June 18 when she was invited, at a time of mushrooming demonstrations against Mr. Morsi’s government, to speak to an audience in Cairo about the United States’ relationship with the Muslim Brotherhood. It was, she said, a welcome chance to “set the record straight.”