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(CNN) -- In May 2003 U.S. President George W. Bush touched down on the deck of the aircraft carrier U.S.S. Abraham Lincoln in a Navy jet inscribed with the words "Commander in Chief" on the cockpit.

Standing underneath a banner reading "Mission Accomplished," he declared the U.S. and its allies had "prevailed" in Iraq.

Almost three-and-a-half years later, with Iraq seemingly locked in a perpetual cycle of violence, Bush is facing growing calls from military leaders and his own political advisors to hit the "mission abort" button instead.

In August John Abizaid, commander of the U.S. Central Command in Iraq, told a Senate committee Iraq was heading towards "civil war."

This month the chief of the British armed forces, General Sir Richard Dannatt, suggested the presence of allied troops was "exacerbating" security problems in Iraq.

Meanwhile a leaked copy of a report by the Congress-appointed Iraq Study Group, chaired by James Baker, the former Secretary of State to George Bush Senior, this week indicated its recommendations could include the large-scale withdrawal of American troops and possibly inviting Iran and Syria -- two countries previously denounced by Bush -- to help in stabilizing the country.

But the most damaging blow to Bush's presidency may yet be dealt by the American public itself.

With mid-term elections next month, the president's popularity ratings are at an all-time low. A CNN poll this week found that 64 percent of Americans now believe going to war was a mistake. (Full story)

If those statistics translate into votes, Bush may well face an uncomfortable final two years in office hounded by a Democrat-controlled Congress.

Yet while many influential figures agree that the time has come for a change of policy in Iraq, the precise details of what such a shift would involve remain unclear.

And although Baker has refused to comment on the exact recommendations the Iraq Study Group will put forward, he has warned there is no "magic bullet" to end the conflict.

For veteran statesmen such as Baker, the parallels with another era-defining American war must also be striking. In the late 1960s the U.S. military found itself fighting an unwinnable conflict, enduring mounting casualties against a growing chorus of dissent at home -- in Vietnam.

On Wednesday Bush himself acknowledged parallels between the current situation in Iraq and the 1968 Tet Offensive -- widely considered to be the point when American public opinion turned against the war.

The U.S. finally extracted itself from southeast Asia in 1973, but only following a pragmatic shift in its conduct of the war. Under President Richard Nixon, American troops were gradually withdrawn and replaced by Vietnamese soldiers.

Nixon, advised by Secretary of State Henry Kissinger, also adopted a more conciliatory policy of "detente" towards Washington's ideological enemies, the Soviet Union and China, ultimately leading to the diplomatic breakthrough that allowed Nixon to claim he had secured "peace with honor."

"What I would imagine America will probably do is what they did before which is to slowly start withdrawing its troops," historian Dominic Sandbrook told CNN.

"George Bush already talks a lot about training up people in Iraq just like Nixon did in Vietnam. What Vietnam teaches us is that sometimes there is no easy answer, there is no strategy for success -- You can get into something and there is no way out."

As recently as August, Bush reiterated his administration's commitment to wage war in Iraq until it had achieved its goals, saying victory would "be a powerful triumph in the ideological struggle of the 21st century... People will look to a democratic Iraq as inspiration that freedom can succeed in the Middle East, and as evidence that the side of freedom is the winning side."

But the Iraq Study Group's report, due before the end of the year, increasingly looks like just the excuse the beleaguered president needs to adopt a more Nixonian approach to foreign policy.

Such a move would also mark the end of the illusion that the conflict in Iraq can be ended by anything as clean-cut as "victory," "freedom" or "democracy."

Vietnam may hold one more lesson for the U.S. however. If its exit strategy from Iraq follows the same course, there is also the danger that the government in Baghdad, on which Washington and its allies have spent so much time, money and blood, may go the same way as the South Vietnamese regime, which collapsed two years after Nixon's "honorable peace."

"The obvious abiding lesson is don't get into these situations in the first place -- don't break something you can't then fix," said Sandbrook. "Vietnam was a good example of that and I don't think they've learnt that lesson."