Washington - Barack Obama will try to pull a fraying country together at a memorial for five slain Dallas policemen on Tuesday - a monumental leadership test as his presidency winds down.Eight years ago, Obama's charisma and ability to inspire propelled him to office as America's first black president, and raised hopes that the country would overcome some of its deeply entrenched societal divides.Even on Saturday, as the country reeled from the Dallas sniper attack targeting police, Obama sounded a note of optimism."I firmly believe that America is not as divided as some have suggested," he told a news conference at a Nato summit in Warsaw. "There is sorrow, there is anger, there is confusion... but there is unity."But soaring words no longer seem enough. America is all too familiar with armed violence, but the country finds itself on a new precipice. From Charleston to Orlando to Dallas, the past year has seen a torrent of slaughter motivated by hate. Each new shooting is borne from a cocktail of toxic political issues that have pitted Americans against each other.They have brought a measure of common revulsion, but not a common purpose.In Orlando, a man pledging allegiance to the Islamic State group shot up a gay nightclub using legally bought automatic weapons. If the combination of sexuality, religion and extremism were not combustible enough, a disturbed black veteran executed five white cops in Dallas last week in the midst of spiking tensions over the fatal police shootings of two black men.Obama will address an interfaith memorial service for the victims and visit with the wounded officers and relatives of the dead on Tuesday.Black and blue lives matter Each week seemingly brings a new shaky image of a white police officer killing a black American that enrages another city.Each new spasm of violence is relived across the country again and again with every click of YouTube or Facebook.America's leaders - their base baying for a hardline stance and their voice diminished by distrust of the political class that permeates western cultures - have struggled to dial back the anger.Obama in particular has struggled most to tether the twin ghosts of race and guns that have been raised in this latest shooting in Dallas. "There is no contradiction between us supporting law enforcement... and also saying that there are problems across our criminal justice system, there are biases - some conscious and unconscious - that have to be rooted out," Obama said."So when people say 'Black Lives Matter,' that doesn't mean blue lives don't matter; it just means all lives matter."Black protest leaders nevertheless accuse him of being too soft on a police force they believe is institutionally racist.Conservative gun-loving Americans are unlikely to listen to Obama for long enough to be coaxed down from the barricades to consider new gun control measures.They deeply mistrust a leader who, even as a candidate trying to win votes, derided them for clinging to guns and religion. The more prejudiced are not going to listen to a black man, full stop.At times, it seems like a dialogue of the deaf.Consoler-in-chief Obama has tried to turn down the volume of the debate by reminding Americans of how much they have in common, by ministering at a time of national crisis.Americans are fundamentally decent, he argues. And 2016 is not like the 1960s, when US cities burned, the Vietnam War raged and the Kennedy brothers and Martin Luther King were slain. Tuesday's address may see more of the same.But even the White House knows that will not break the logjam.At best, it could reassure the unproblematic middle, not the hardliners who must be brought into the fold.At worst, the optimistic message will seem dangerously out of touch to Americans reeling from one atrocity after another.With an election less than four months away, Americans could expect a new group of leaders to come forward.But Democratic candidate Hillary Clinton - in this bitter climate and with 30 years served in the political trenches - may equally struggle to bridge ideological fault lines.Republican presidential candidate Donald Trump appears not to want to try."President Obama thinks the nation is not as divided as people think. He is living in a world of the make believe!" tweeted Trump.Obama, perhaps sensing that more divisive voices could fill the political void, uncharacteristically decided to cut short a visit to Spain and return to the United States a day early.That in itself could be seen as an indictment of Clinton's inability to take up the mantle.