Washington (CNN) In Washington, political alienation is now so intense that the world's most powerful nation can't agree how to keep its next generation safe in school -- or fix the system regulating immigration, the human lifeblood which has been America's foundation.

The frozen, acrimonious politics of Capitol Hill and the antagonism of a White House that knows only how to attack were exposed Thursday as Americans tried to process the horror of kids mercilessly killed in yet another school massacre.

Then, in another dereliction of duty, lawmakers and the Trump administration combined on another abject failure -- to deal humanely with the hundreds of thousands of people, brought illegally to the country as kids.

It was the latest great fail over the last three administrations by Congress to reform the immigration system -- amid differences apparently too poisonous to be bridged -- and left senators shaking their heads and wondering where to go next.

Neither the misery of those bereaved by the Florida school massacre nor the agony of the Dreamers could shake Washington's warring politicians from the entrenched positions of a dispiriting era devoid of the compromise meant to grease American governance and actually make things work.

The most searing image of the day came as the mother of a young girl gunned down in her classroom on Wednesday, tortured by grief, berated President Donald Trump in an extraordinary moment on CNN.

"President Trump, please do something! Do something. Action! We need it now! These kids need safety now!" Lori Alhadeff screamed.

"President Trump, you say what can you do? You can stop the guns from getting into these children's hands," she said. "What can you do? You can do a lot! This is not fair to our families and our children to go to school and have to get killed!"

It was a harrowing cry that did not just encapsulate a mother's grief but was a non-partisan indictment of a political system that appears unable to help many of the people on whom it depends for legitimacy and that is drained of the trademark optimism and can do spirit that made America a superpower.

Vacuum of leadership

JUST WATCHED Trump addresses nation in wake of shooting Replay More Videos ... MUST WATCH Trump addresses nation in wake of shooting 06:28

Trump, finally, stepped up to console the nation, nearly 20 hours after the massacre that killed 17 children and staff.

He's not yet at ease in the role of the nation's emotional shepherd. But he offered an effective and sometimes moving homily, seeking to bring people together -- even if he could not make sense of the carnage.

"I want you to know that you are never alone and you never will be," he told the children of America, who have to go to school and endure active shooter drills and wonder whether they will be coming home at night.

"You have people who care about you, who love you and who will do anything at all to protect you," Trump said, in remarks that were touching in part because they were such a departure from his normal acerbic tone.

But Trump left a vacuum of leadership because he was unable to answer the question of people like Alhadeff.

He only offered a vague pledge to make schools safer, and to tackle mental health -- but by omitting to even mention the nation's guns laws, made clear that any objective consideration of any necessary changes is off the table.

The President had already undermined his own ministrations when earlier on Thursday he indulged in a characteristic blame shifting exercise, singling out the residents of ill-starred Broward County.

"So many signs that the Florida shooter was mentally disturbed, even expelled from school for bad and erratic behavior," Trump tweeted. "Neighbors and classmates knew he was a big problem. Must always report such instances to authorities, again and again!"

So many signs that the Florida shooter was mentally disturbed, even expelled from school for bad and erratic behavior. Neighbors and classmates knew he was a big problem. Must always report such instances to authorities, again and again! — Donald J. Trump (@realDonaldTrump) February 15, 2018

Republicans control all the power in Washington. So they for now must take most of the blame for the paralyzing dysfunction.

As incumbents they could pay a price in November's midterm elections, yet since the nation is so split, the polls may simply end up solidifying the polarization.

The problem is deeper than any one party or any one leader, following several decades where each side has run in elections and governed for their base and major legislation gets jammed through on party-line votes.

Coastal liberals, meanwhile, have often seemed to look down on those who do no share their progressive inclinations -- and cling to "guns or religion" as Barack Obama once put it -- so are partly to blame for the political distemper that led to Trump's anti-establishment blitzkrieg.

No new thinking

JUST WATCHED Rubio: Not fair to blame lawmakers after attack Replay More Videos ... MUST WATCH Rubio: Not fair to blame lawmakers after attack 01:44

Still, anyone who had hoped that new horror would promote new thinking and a burying of partisan differences was disappointed on Thursday.

Conservatives like Texas Sen. Ted Cruz and House Speaker Paul Ryan were quick to warn that Democrats must not use the tragedy to think about depriving anyone of their Second Amendment rights.

"This is one of those moments where we just need to step back and count our blessings," Ryan said, before making it clear that the solutions that Democrats might offer, more gun control or background checks were not acceptable.

Florida Sen. Marco Rubio maintained that gun restrictions could not have prevented Wednesday's bloodbaths -- remarks that will raise eyebrows abroad, where firearms are hard to come by and school massacres are rare.

The White House noticeably canceled its briefing for the second straight day Thursday, sparing itself questions about exactly how it was going to implement what officials said was a "plan that works" to stop school shootings.

After the Las Vegas massacre that killed 58 people last year, White House press secretary Sarah Sanders had rebuked reporters, saying there was a "time and a place for a political debate" about guns, but not right after an attack.

Democrats slipped into their usual rituals after a mass shooting, questioning why anyone would need a gun so powerful that it can wipe out innocents in an instant.

"Children are dying in our schools, in our communities, on our streets. All this Congress has to say is, 'Let's have a moment of silence,' " said Nancy Pelosi, the House Democratic leader.

Democratic Sen. Dianne Feinstein voiced frustration at a system that cannot agree to do anything after regular gun massacres.

"Doing nothing is not the answer -- there will just be more," she said.

No one says fixing gun violence will be easy or that anyone on either side has all the right answers.

It's easy to call for secure schools -- much harder to do it. The often sprawling buildings with multiple exits, where pupils can simply be sitting ducks would require a massive building program of fortresses along the lines of terror proof US embassies abroad. There seems to be little appetite in Washington to fund such an undertaking.

But the message from Thursday was that Washington's politicians don't trust one another enough to even try -- and that might be the worst thing of all.

Sense of despair

On immigration, there was a similar sense of despair from those who have tried for years to soothe a a national fault line.

"I don't know where we go from here," said Sen. Lindsey Graham, R-South Carolina, an immigration reform advocate.

The spectacle of utter futility was if anything more infuriating than the impasse on how to stem the rash of mass shootings.

The administration, turning scorching fire on Republicans seeking compromise defeated a bipartisan attempt to shield Deferred Action for Childhood Arrivals program recipients in exchange for funding for the President's border wall.

But the administration's own hardline plan, which would have overhauled legal immigration as well, tumbled to an even more stinging defeat.

So the White House killed a potentially workable compromise but has no way to advance its own proposal bringing a crucial debate -- with Dreamers at risk of losing their right to work and study in the US -- crashing to a halt.

Several Republican senators, including Susan Collins of Maine, were left fuming after the White House scuttled the compromise bill.

When he was taking about the Florida massacre, Trump sought to bring the country together, but he could have been talking about immigration, too.

"It is not enough to simply take actions that make us feel like we are making a difference. We must actually make that difference," said the President.

It's anyone's guess how.