"Maybe I should just pack up and go home. Golly," said Obama, probably thinking the question impertinent, since he is only three months into his second term.
"As Mark Twain said, rumors of my demise may be a little exaggerated at this point," Obama said.
Yet Obama, even as he woos lawmakers with trips up Capitol Hill and intimate dinners, can barely contain his contempt for Congress, which blocks him at every turn and threatens his hopes for a robust second-term. Read: Obama cautious but hints at eventual action on Syria
"My charm offensive has helped me learn some interesting things about what's going on in Congress -- it turns out, absolutely nothing," Obama said Saturday.
President Barack Obama answering questions during his new conference in the Brady Press Briefing Room of the White House in Washington. AP
The president's joke, at the White House correspondents dinner, betrayed frustration at banging his head against a congressional brick wall.
"You seem to suggest that somehow these folks over there have no responsibilities and that my job is to somehow get them to behave," Obama told reporters Tuesday, in a snipe at lawmakers.
In March, he had told Israeli Prime Minister Benjamin Netanyahu moments after touching down in Tel Aviv: "it's good to get away from Congress." Read: At reporters’ dinner, Obama tickles audience
Obama's cynicism is distilled from disappointment: he said while running for re-election last year that his victory could cause the Republican "fever" to break and catalyze more cooperation in Congress.
Apart from an end-of-year deal on allowing Bush-era tax cuts on the rich to expire, Republicans have dug in their heels on multiple fronts.
Obama's gun reform drive after the Newtown school massacre foundered mostly on Republican opposition -- though some conservative Democrats peeled away. Read: FBI did what it was supposed to do in Boston bombing case, says Obama
Chances of a deficit-cutting "grand bargain" are slim and discord between Obama and Republicans triggered $87 billion in automatic spending cuts known as the "sequester."
US President Barack Obama is pictured as first lady Michelle Obama speaks during an event on finding employment for military veterans. Reuters
Obama vowed to make a new push to close Guantanamo Bay on Tuesday -- but the odds that Congress will change its mind and let him do so are extreme. Read: Obama renews vow to close Guantanamo detention camp
One ray of light though is Obama's top second-term priority -- immigration reform which key Senate Republicans know they must support if they are to win back Hispanic voters and have a viable path in future presidential elections.
The legislation's prospects in the Republican-led House of Representatives, though appear unclear.
All second term presidents race the clock as their influence wanes.
Former George W Bush advisor Karen Hughes, who saw her boss fail in his second term to reform immigration and social security, told NBC Sunday that re-elected presidents have only a year to pass their program.
Still, while Obama's influence may ebb at home -- the US commander-in-chief is never irrelevant and second term presidents often look abroad to build their legacies.
Obama parried questions Tuesday about whether he will intervene in Syria, after the apparent use of chemical weapons there contravened a "red line" he laid down last year.
US vice president Joe Biden shares a light moment with US President Barack Obama during an event on finding employment for returning military veterans from their service, in the East Room of the White House in Washington. Reuters
He must also make hugely consequential decisions on Iran's nuclear program and the withdrawal from Afghanistan.
His covert drone war will likely continue to the end of his presidency in 2017 and he is expected to travel this year to Europe twice, mount a major African tour and return to Asia in October.
And as the Boston bombings and other recent tragedies showed, the US president often takes on a role of national counseler.
Earlier presidents can also testify that sometimes the press is too early to confer lame duck status.
"The president is relevant here," president Bill Clinton declared in April 1995, during a miserable political run.
A day later, a bomb ripped through a federal building in Oklahoma City sparking a national crisis that not only showcased Clinton's relevancy, but helped him relaunch his presidency – and win re-election.
In October, 2007, Bush vowed "I'm going to sprint to the finish, and finish this job strong, that's one way to ensure that I am relevant."
The following year, amid the election for the man who would replace him, Bush was back at center stage, flexing the powers of the presidency to try to stave off a financial meltdown.
And if any president ran to the finish it was Clinton, who unsuccessfully pursued a deals on Middle East peace, and ending North Korea's missile program, right up to the end.