Rarely has a president been handed such a gift in the runup to an election year as the death of Osama bin Laden

How sweet it was on Saturday night for Barack Obama to be able to take to the stage at the White House correspondents' dinner in Washington and mock his would-be nemesis, Donald Trump, for having embraced the birther conspiracy, which the president scotched only last week with the production of his birth certificate.

That was nothing compared with the sweetness of the moment that came 24 hours later when Obama took to the national stage, announcing from the east wing of the White House that he had successfully ordered the killing of Osama bin Laden.

That address, delivered sombrely but with evident relish by Obama, will almost certainly dash any remaining hopes on Trump's part that his wife, Melania, will be choosing new curtains for the White House in 2013. It may also sweep away the aspirations of several other potential Republican candidates hoping to limit Obama to one term.

Rarely has an incumbent president been handed such a gift in the runup to an election year. As the huge crowd that assembled outside the White House testified, "getting Osama" is grounds for national jubilation.

Larry Sabato, professor of politics at the University of Virginia, tweeted: "This is a giant political plus for Barack Obama. Almost 100% of Obama's political enemies will cheer him for this one. Imagine the 2012 TV ad."

Another political scientist, Ross Baker of Rutgers University, told Politico: "The domestic political implications are considerable. For generations the Republicans have painted the Democrats as soft on national security and hostile toward the military.

"This will hinder the GOP [Republican] attack, allow Obama to be more closely identified with the military in the eyes of the public. Whatever consequences it may have in the war on terrorism, it is a coup for Obama and Democrats politically going into 2012."

Even Obama's arch-critic Glenn Beck said on his radio show: "Thank God we have a president who actually authorised the shoot-to-kill. That is a surprising shock to me. And I think that deserves to be said that I didn't think that this president would actually ... have somebody pull the trigger. And he did. Congratulations, President Obama. Thank you for doing the right thing on this."

Former Vice President Dick Cheney, the Republican who emerged as Obama's chief critic on national security matters, offered praise. "President Obama and his national security team acted on the intelligence when it came in and they deserve a lot of credit, too," Cheney said.

Obama was at pains in his announcement to emphasise the personal role he had played as commander-in-chief. He underlined that he had ordered the CIA to make the killing or capture of Bin Laden its top priority; that he had met repeatedly with the national security team when the al-Qaida leader's whereabouts had become known; and that it was at his direction that the operation to assassinate Bin Laden was launched.

The accent on his firmness in the face of the terrorist threat is unlikely, in the case of Bin Laden, to displease even the most liberal of Democratic voters, who have grown increasingly despondent about the president's refusal to break with the central features of George Bush's war on terror, such as the maintenance of the detention camp at Guantánamo Bay. It is likely to play very well with independent voters, upon whom his re-election depends.

In his wording, it was clear that Obama was seeking to put to rest the comparison with Jimmy Carter, the last Democrat to be thrown out of the White House after just one term, which has dogged his presidency.

Obama stressed that none of the US special forces had been harmed in the operation to kill Bin Laden, an allusion to Carter's disastrous attempt in 1980 to rescue the Iranian hostages that cost American lives.

Obama will be hoping that the feelgood fallout from the news of Bin Laden's death will lead to a bounce in his popularity ratings, which have remained worryingly low for many months. In the latest Rasmussen poll, 49% of voters said they disapproved of his leadership – 37% strongly – although that was before this weekend's events in Pakistan.

On the other hand, the polls show consistently that the top priority for voters is no longer national security, which almost 10 years after 9/11 has waned as a preoccupation, but the economy.

With petrol prices at a historic high, and unemployment still at 9.2%, Obama will know that even the death of Bin Laden will not secure him a second term unless the economy improves.

At least now, though, he has the pleasure of watching his opponents squirm. The announcement saw Republican 2012 hopefuls reaching for the superlatives. Among them was Mitt Romney, who called the news "a great victory for lovers of freedom and justice everywhere".

The gloves won't stay off for long. But for now, Obama can enjoy being on top.