GEOFF BENNETT: On a crucial visit to Washington today, Ukrainian President Volodymyr Zelenskyy met with President Biden in the Oval Office and then Vice President Kamala Harris for in-person requests for more military and economic aid as part of what he calls a victory plan.

AMNA NAWAZ: President Biden announced $8 billion in military aid to Ukraine, much of which is for already authorized weapons.

But certain key features of the new aid include another Patriot missile defense battery, precision-guided glide bombs with a range of 81 miles, more F-16 pilot training, and American investment to help Ukraine's defense industry.

What did not come out of today's meeting?

U.S. permission to fire American weapons deep inside Russia.

VOLODYMYR ZELENSKYY, Ukrainian President: Today, we have a new strong support package, as you said, and we have common view on the things that need to be done.

We have to keep pressure on Russia to stop the war and to make truly lasting and just peace.

KAMALA HARRIS, Vice President of the United States (D) and U.S. Presidential Candidate: There are some in my country who would instead force Ukraine to give up large parts of its sovereign territory, who would demand that Ukraine accept neutrality and would require Ukraine to forego security relationships with other nations.

These proposals are the same of those of Putin.

AMNA NAWAZ: Zelenskyy will meet with former President Trump tomorrow.

But far from the political grappling here, there's a battle for air superiority that's crucial along the front lines in Eastern Ukraine.

Russian glide bombs launched from aircraft lay waste to Ukrainian positions and to the towns nearby.

And a harrowing game of cat and mouse is being played with kamikaze drones, up close, personal and terrifying.

GEOFF BENNETT: The drones are mostly consumer drones with deadly explosive accessories.

They create havoc and instill terror among the forces along the front lines.

Special correspondent Jack Hewson traveled recently to Toretsk to witness this deadly face-off.

And a warning: Images in this report may disturb some viewers.

JACK HEWSON: We're following a drone unit into the town of Toretsk 1.2 miles from the Russian line.

You can hear a lot of outgoing fire from this position, nothing incoming yet, but you can tell from just the tick and noise of how close we are to the hard front.

Drones have made the front so lethal that we must move by night.

Even then, some have thermal cameras that see in the dark.

Suddenly, we hear a noise that soldiers have come to fear.

For a moment, we freeze.

But we're lucky.

These are the Ukrainian teams' drones returning home, and we move safely below ground.

First-person-view drones, or FPVs now stalk infantry, not just high-value targets.

The way war is waged has been transformed.

There are so many FPVs in the sky that individual soldiers are now hunted, like these Russian infantrymen caught in open ground, a dystopian video game with real-world kills.

At dawn, the unit emerges into the light.

We have been taped up green to indicate we're not Russian soldiers.

Right now, these guys are preparing a drone for a mission to target a Russian position.

You can see he's attaching an explosive charge to the bottom of a Mavic DJI drone, shortly after which they're going to launch it.

BORZI, Armed Forces of Ukraine (through translator): The drone is armed now.

And don't worry.

It's our artillery you can hear.

JACK HEWSON: This team alone claims to fly more than 50 of these sorties every day.

The pilot, call sign Borzi, shows us a clip of his team killing Russian infantry dropping explosives wrapped with shrapnel, modern warfare as detached and remote as it is brutal.

When you're dropping these on Russians, what do you think?

BORZI (through translator): I'm thinking about how to help my friends, the infantrymen.

I'm defending what's mine, my territory.

So I don't feel anything at all.

JACK HEWSON: Ukraine's drone teams punch above their weight, but they can't compete with conventional Russian airpower, particularly glide bombs.

Carrying up to 1.2 tons of explosives and launched from far behind the Russian line, they glide onto their targets, devastating Ukraine's defensive positions and obliterating front-line towns.

ULTRA, Armed Forces of Ukraine (through translator): The Russians currently have an advantage in the air.

They completely destroy the area they want to take over with guided air bombs.

We cannot stand against the amount of airpower directed at us.

We just physically cannot do it.

JACK HEWSON: It's time to go.

In Toretsk, it's safer to not stay in one place for too long.

The drone team move to a new basement every few days.

OK. We have got to run for the car.

We have to be quick.

In broad daylight and with clear skies, we're visible and exposed.

Once a town of 30,000, now a ruin.

Look at the destruction.

There's not a lot left in the city.

We're leaving at serious pace, because we're still within range of potentially being hit by Russian FPV drones.

This vehicle's got jammers, but we're taking no chances.

Jammers scramble drone broadcast frequencies, but they change daily.

You can still be hit.

It's a nerve-shredding gauntlet soldiers run daily.

At a stabilization point 12 miles away, the new arrivals bear the wounds of an army stretched to its limit, flesh ripped, punctured and torn.

Russia's superior numbers, ammunition and airpower are taking a withering toll on Ukraine's troops.

Every day there are more, says Denis, a medical group commander with the 5th Assault brigade.

DENIS, Medical Group Commander (through translator): Most of the wounds are from shrapnel.

This is the largest percentage among all injuries.

The percentage of bullet wounds is less now because there are fewer such assaults now.

And we attack the Russians more with drones than with bullets.

JACK HEWSON: The endless trauma is exhausting, and polls show more Ukrainians are starting to consider the possibility of negotiating peace.

But despite all this spilt blood, the majority still want no concessions.

They want to fight on.

Denis has no time for those with war fatigue.

DENIS (through translator): Here, you can be angry and tired to the bone.

You can be exhausted.

You can be aggressive.

You can hate everything, but not fatigued.

You see, when it's a matter of survival, you have no right to allow yourself to get fatigued.

We can only allow ourselves that feeling when we're at home and in peace.

JACK HEWSON: Outmanned and outgunned, Toretsk may soon fall, like several other key Donbass towns.

But, for now, Ukraine battles on, seemingly through bloody-minded determination alone.

For the "PBS News Hour," I'm Jack Hewson in Toretsk, Ukraine.