WASHINGTON (Reuters) — President George W. Bush is facing a moment of truth over Iraq but is showing no sign that he will buckle under the pressure and embark on a new strategy in the unpopular war.Iraq looms over Bush’s presidency. It has driven down his poll numbers and he sheds tears over soldiers dying there and in Afghanistan.

But people who have visited with him say that for a president besieged, Bush remains remarkably self-assured, confident that history will prove him right.

He seems convinced that to engage in a precipitous withdrawal would leave Iraq open to becoming a safe haven for September 11-style attackers, even though critics say that is precisely what the Iraq invasion produced.

A reader of history, Bush occasionally brings to the White House groups of scholars to discuss its lessons. Iraq usually comes up.

Irwin Stelzer, an economic expert at the Hudson Institute in Washington, was invited to one session and found that Bush exuded “a calm feeling that having done what’s right, the rest will take care of itself”.

“I didn’t get the feeling of beleaguered or some of those photos you see of Richard Nixon when things were coming apart. There was none of that.”

Bush wanted to know why the United States was not more popular in Europe and chuckled when he suggested it was his personality. Stelzer told Bush he agreed: “It’s probably your personality.”

Stelzer also told Bush, “I think Europeans don’t relate as well to Texans as they do people from Boston. But secondly, it’s Iraq. People disagree with the policy.”

Democrats failed to muster the votes earlier this year to set a timetable for withdrawing the troops. Now they are mounting a new effort to force Bush to start bringing them home.

A report on Bush’s troop buildup this year — due out this week — will give them ammunition. It will offer a mixed picture that the Iraqi government is making progress in some areas but no headway on meeting political benchmarks set by the United States.

“Our message to the president is clear. It is time to begin ending this war — not next year, not next month — but today,” said New York Democratic Sen. Hillary Clinton, who is running to replace Bush in the November 2008 election.

Don’t listen to the Democrats, say the conservatives. Let the troop buildup have time to work, or else Bush will “be viewed as a feckless, irresolute president, incapable of seeing his own strategy through,” wrote William Kristol, editor of the conservative Weekly Standard.

The key to forcing Bush to accept a shift in strategy probably lies with his fellow Republicans, and whether the wavelet of defectors becomes a tsunami.

So far a small group of influential Senate Republicans — including Richard Lugar of Indiana, Pete Domenici of New Mexico and George Voinovich of Ohio — have bolted.

Others are grousing, working on bipartisan approaches that try to bring Bush back to last December’s Iraq Study Group report that said all US combat troops could be out of Iraq by March 2008.

Lee Hamilton, a co-author of the Iraq Study Group report, thinks that is still a good idea.

“I don’t think it’s too late, but there are certainly those who say this situation is certainly beyond repair and we had better just get out,” Hamilton said. “That opinion is probably growing, but I don’t think it’s a majority opinion.”

Bush says he would like to get to the Iraq Study Group recommendations eventually, but the violence must ease first.