WASHINGTON — Senator Elizabeth Warren, the Massachusetts Democrat whose vituperations against Wall Street have helped push her party to the left, has no official role opposing President Obama’s trade agenda.

She does not sit on the committee where the trade package was written. She has never taken part in negotiations over its legislative language. When Democrats held a news conference after the measure failed on a procedural vote Tuesday, she was not there, nor did she speak on the floor after it passed on Thursday, as many of her colleagues did.

Yet it is Ms. Warren who has become the national face of opposition to Mr. Obama on the trade package. She was the focus of the president’s ire last week when he attacked fellow Democrats as wrongheaded after his efforts to woo his party on the issue went nowhere.

“The truth of the matter is that Elizabeth is, you know, a politician like everybody else,” the president said in widely quoted remarks.