Putin sent troops into Crimea this month after the president of Ukraine, a Putin ally, was overthrown in a revolt. Most in Crimea are of Russian descent. Over the weekend, they voted to join Russia.
Ukrainian troops are still on their bases in Crimea, and for the first time, there was some shooting Tuesday, with one killed.
It's unclear why a shooting broke out in the capital, but Ukrainian defense sources say unidentified armed men stormed a Ukrainian base.
Thousands of Ukrainian soldiers are barricaded in on their bases all over the Crimean peninsula. Behind makeshift blockades, they're on constant alert, surrounded by hostile pro-Russian armed men.
CBS News arrived Tuesday night at one such base where soldiers feared an attack was imminent after they had refused to surrender. At first, an officer wanted to speak with CBS News, but suddenly, an armed man loomed out of the dark and told him to keep his mouth shut.
After phoning his commander, the Ukrainian said it was too dangerous and that CBS News should leave.
The longer this situation festers, the riskier it becomes, especially after Ukrainian defense department authorized its soldiers to use their weapons to defend themselves.
Russia has massed troops all along its border with Ukraine, and there are worries the annexation of Crimea is only the start.
Along the border of Russia, Ukrainian forces are getting ready for war, Charlie D'Agata reports. Sasha and Frerdo are childhood friends from Donetsk. They found little in President Vladimir Putin's speech to like.
"The biggest lie is that he respects the Ukraine, that he still believes that Russians are our older brothers and that we have to live with Moscow or don't live at all," Sasha says.
He says he takes Putin's comments as a warning that the Russian takeover of Crimea is just the beginning.
They're both fathers of young children. Like many in Donetsk, they describe themselves as half Ukrainian, half Russian.
"The biggest sin of Mr. Putin is he provoked this fight between brothers," Frerdo says.
Brothers or not, Ukraine's defense minister has put the call out for tens of thousands of volunteers to take up arms in case of a Russian invasion.
"I am not ready to fight with Russians, with Ukrainians," Sasha says. "I don't want to die for our country, I want to live for our country."
They're worried about relatives who live in Crimea -- who now live in another country.
Frerdo says he doesn't think Ukraine will ever get Crimea back.
CBS News asked both men whether they would leave if fighting broke out in Donetsk, and they were torn between their responsibilities to protect their families and their duty to protect their country. They couldn't answer.