Putin is on the rocks, and Ukraine is surging. If U.S. support stays strong, Kyiv can win.

Last week was a turning point in Russia’s war on Ukraine. Kyiv’s astonishing gains will continue, and it is possible to envision a Ukrainian victory, so long as its Western supporters don’t lose their nerve.

After staging sham referendums at gunpoint in four occupied Ukrainian regions, Vladimir Putin announced Friday that residents had “chosen” to rejoin their “historic [Russian] motherland.” At a televised pop concert Friday in Red Square, he celebrated the forced annexation and led the chant of “Russia, Russia,” shouting exuberantly, “Welcome home!”

The very next day, Saturday, Ukrainian forces made stunning advances in the east and south, taking back land within the “annexed provinces” and breaking through Russian lines as they had in Kharkiv province earlier in September. Suddenly, over the weekend, the tightly controlled Russian airwaves that only broadcast Russian “victories” featured talk show debates over how to stem Russian losses.

» READ MORE: Putin's nuclear threats are a sure sign his war on Ukraine is failing. | Trudy Rubin

Yet once again, Putin is hinting he might use nukes if desperate. Some of his acolytes are calling on him to use “tactical nuclear weapons.”

So where does Putin’s war go from here? Here are a few of the key questions and how I size up where things stand.

They are demonstrating that they can win — if Western support remains strong and new weapons arrive in time.

Putin’s imperialist call to restore the “unity” of “great historic Russia” revealed a total misunderstanding of the Ukrainian people. He conveniently ignored the fact that, in 1991, in a genuine referendum, every region of Ukraine voted overwhelmingly for independence from the Soviet Union (the four Putin annexed voted in 1991 by margins of 90%, 90%, 83%, and 83%). Even Crimea voted 54% to join an independent Ukraine.

So Ukrainians rightly believe they are waging an existential battle for their freedom, while many Russian conscripts are unsure why they are fighting. As Secretary of State Antony Blinken put it succinctly, “If Russia stops fighting, the war ends. If Ukraine stops fighting, Ukraine ends.”

Russian troops are demoralized. The Russian military system has become so disorganized that new troops are told to bring their own sleeping bags and food, and sent in with little or no training. Resistance is growing in Russia to Putin’s new, unjust mobilization of at least 300,000 new forces, from which hundreds of thousands are fleeing abroad.

New precise Western long-range multiple rocket systems with a range of 50 miles, especially the U.S.-built weapons known as HIMARS, have enabled Ukraine to disrupt Russian supply lines and command centers behind the front lines. The U.S. just announced it will send four more HIMARS to Ukraine; it should also expedite the arrival of long-range munitions for the launchers. Sending as much vital weaponry as possible before winter, and before the arrival of newly mobilized Russians, is key.

However, Russia still holds over 15% of Ukrainian land, and its missiles and rockets are destroying civilian infrastructure across the country. “They are killing ordinary families and children every night in our cities,” I was told on WhatsApp by former parliament member Yehor Soboliev, who volunteered for military service. “We will win in any case, but we will meet many more deaths,” he said.

Kyiv military sources tell me their greatest need right now is for air-defense systems to protect their cities, and for tanks (where are those Leopard tanks, Germany?) to roll back fortified Russian positions as Ukrainian troops move forward on the flat steppe lands of the east and the south.

I am still skeptical that this will happen.

In military terms, it makes no sense. These weapons, with a much smaller payload than the Hiroshima bomb, are meant for the battlefield. But as the Institute for the Study of War, one of the best think tanks closely following the fighting, puts it: “The Russian military in its current state is almost certainly unable to operate on a nuclear battlefield even though it has the necessary equipment. Exhausted contract soldiers, hastily mobilized reservists, conscripts and mercenaries … could not function in a nuclear environment. Any areas affected by Russian tactical nuclear weapons would thus be impassable for the Russians, likely precluding Russian advances.”

» READ MORE: Putin's war on civilians hardens Ukraine's military resolve. | Trudy Rubin

Moreover, the wind could blow radiation back onto Russian troops or even inside Russia. And if a tactical nuclear weapon were dropped on a city, killing, say, 5,000 to 10,000 civilians, Russia would become a global outlaw, even to India and China. And the Ukrainians would keep fighting.

That said, the U.S. and its allies must leave Putin in no doubt that there would be “catastrophic consequences for Russia” — as national security adviser Jake Sullivan put it on ABC News — if Russia breaks the post-World War II taboo against nuclear weapons, plunging the world into a new nuclear era. That doesn’t necessarily mean a nuclear response, but it should mean military strikes by NATO members on Russian bases inside Ukraine, Russian ships in the Black Sea, and possibly on Russian bases in the homeland. It should also finally trigger a NATO invitation to Ukraine.

“Putin has to know it would be a suicide weapon for them,” I was told by H.R. McMaster, a former national security adviser in the Trump administration. Yes, indeed.

In a historic first joint visit to Pennsylvania Monday, a large group of ambassadors from European Union countries insisted that Europe would hold firm in support for Ukraine, despite the pain of skyrocketing gas prices, and despite far-right gains in Swedish and Italian elections. Speaking to the Foreign Policy Research Institute and the World Affairs Council of Philadelphia, Stavros Lambrinidis, the EU ambassador to the United States, said, “Putin cannot win this. It is existential to all of us. This is not a war against Russia. It is a battle for values. You don’t invade to wipe countries off the map.”

Ukrainian courage and strategic skills, combined with Western intelligence-sharing, have opened the way for a Ukrainian victory before winter. All now depends on whether Western allies have the guts to match their Ukrainian compatriots with vital weapons and a united front against Putin. Kyiv is fighting not just for Ukraine’s freedom, but to prevent Putin from threatening Europe and, inevitably, the United States.