President Barack Obama’s stunning announcement that U.S. forces had killed Osama bin Laden is first and foremost an enormous American victory that eliminates a vicious adversary who both masterminded anti-Western terrorism and symbolized the dark side of Islamic fundamentalism.

But bin Laden’s death also has important domestic political implications.

Though unlikely to become the centerpiece of Obama’s 2012 re-election campaign, as George W. Bush stressed his post-9/11 leadership in 2004, it provides a powerful boost for Obama’s standing as a strong leader and counters frequent Republican charges that he’s indecisive.

And it shows the problems GOP hopefuls face in challenging an incumbent president, as was clear in the somewhat strained statements several issued after the Obama’s surprise announcement Sunday night.

Obama’s success came against a backdrop of his difficulties in trying to complete the U.S. withdrawal from Iraq, lay the stage for starting a similar drawdown from Afghanistan and cope with the complex Libyan situation without becoming enmeshed in another major war or failing to protect insurgents trying to overthrow Moammar Gadhafi.

Indeed, it may help Obama follow through on his promise to begin withdrawing U.S. forces from Afghanistan this summer.

And his announcement that U.S. forces had killed the modern-day mastermind of international terrorism came just 66 years after the announcement of the death of another purveyor of mass evil, Nazi Germany’s Adolf Hitler.

It also came eight years to the day after Bush famously proclaimed a premature end to military operations in Iraq beneath a sign declaring, “Mission Accomplished.”

Obama asserted, from the outset, that he had made bin Laden’s killing or capture “the top priority of our war against terror,” a statement that could be seen as veiled criticism of Bush for over-stressing Iraq or continuity with his predecessor’s vow to get bin Laden “dead or alive.”

On Sunday, Obama phoned Bush, who responded with a warm statement calling it a “momentous achievement” and congratulating Obama “and the men and women of our military and intelligence communities who devoted their lives to this mission.”

Former Vice President Dick Cheney also commended Obama, as did House Speaker John Boehner, 2008 Obama rival John McCain and some potential presidential candidates, including developer Donald Trump, former Speaker Newt Gingrich and former Minnesota Gov. Tim Pawlenty.

Other Republicans, including several 2012 hopefuls, either downplayed — or totally withheld — any direct references to Obama, lest they say something too complimentary about the man they hope to unseat.

Former Massachusetts Gov. Mitt Romney congratulated “our intelligence community, our military and the president.”

Former Alaska Gov. Sarah Palin, former Arkansas Gov. Mike Huckabee, Minnesota Rep. Michele Bachmann and former Pennsylvania Sen. Rick Santorum limited their comments to praising military and intelligence operatives.

Though Obama’s poll standings rose immediately, the longer political impact may be harder to figure. After all, domestic issues still expect to dominate the 2012 campaign, and bitter budget battles lie ahead.

But bin Laden’s death gives Obama a tangible boost in one historically accurate measure of presidential re-election prospects: American University historian Allan Lichtman’s system that rates an incumbent in re-election trouble if at least six of 13 “keys” to the presidency turn against him.

Some are pre-determined by such factors as a president seeking re-election and the GOP gaining mid-term election House seats. But others hinge on events, including two on the economy and two on foreign policy.

So far, Obama had done well on one foreign policy “key” by avoiding a foreign or military disaster but less well on the one rewarding a major success. Bin Laden’s death assures him that signal achievement.

It’s just one more reason why David Gergen, a top White House aide for both Republicans and Democrats, said on CNN, “It’s the best night of his presidency.”