WASHINGTON — President Obama had not even taken office before supporters were etching his likeness onto Mount Rushmore as another Abraham Lincoln or the second coming of Franklin D. Roosevelt.

Yoichi R. Okamoto/LBJ Library Collection

Presidents Johnson and Eisenhower in 1968.

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U.S. Army

Helicopters in South Vietnam in 1971.

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Tyler Hicks/The New York Times

DANGER ZONE American soldiers, dropped by helicopter, patrol a volatile area about 9,000 feet up a mountain known as Sawtalo Sar in the Korengal Valley.

Yet what if they got the wrong predecessor? What if Mr. Obama is fated to be another Lyndon B. Johnson instead?

To be sure, such historical analogies are overly simplistic and fatally flawed, if only because each presidency is distinct in its own way. But the L.B.J. model — a president who aspired to reshape America at home while fighting a losing war abroad — is one that haunts Mr. Obama’s White House as it seeks to salvage Afghanistan while enacting an expansive domestic program.

In this summer of discontent for Mr. Obama, as the heady early days give way to the grinding battle for elusive goals, he looks ahead to an uncertain future not only for his legislative agenda but for what has indisputably become his war. Last week’s elections in Afghanistan played out at the same time as the debate over health care heated up in Washington, producing one of those split-screen moments that could not help but remind some of Mr. Johnson’s struggles to build a Great Society while fighting in Vietnam.

“The analogy of Lyndon Johnson suggests itself very profoundly,” said David M. Kennedy, the Stanford University historian. Mr. Obama, he said, must avoid letting Afghanistan shadow his presidency as Vietnam did Mr. Johnson’s. “He needs to worry about the outcome of that intervention and policy and how it could spill over into everything else he wants to accomplish.”

By several accounts, that risk weighs on Mr. Obama these days. Mr. Kennedy was among a group of historians who had dinner with Mr. Obama at the White House earlier this summer where the president expressed concern that Afghanistan could yet hijack his presidency. Although Mr. Kennedy said he could not discuss the off-the-record conversation, others in the room said Mr. Obama acknowledged the L.B.J. risk.

“He said he has a problem,” said one person who attended that dinner at the end of June, insisting on anonymity to share private discussions. “This is not just something he can turn his back on and walk away from. But it’s an issue he understands could be a danger to his administration.”

Another person there was Robert Caro, the L.B.J. biographer who was struck that Mr. Johnson made some of his most fateful decisions about Vietnam in the same dining room. “All I could think of when I was sitting there and this subject came up was the setting,” he said. “You had such an awareness of how things can go wrong.”