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The relationship between President Obama and Russian President Vladimir Putin appears to have reached the breaking point over the crisis in Ukraine.

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Through a series of long telephone conversations, Obama and Putin have talked extensively behind the scenes about the fate of Crimea, with the United States repeatedly warning Russia against a grab for territory.

But Putin appears to be forging ahead, defying Obama’s calls for a diplomatic solution that would allow both sides to save face.

Now the U.S. and its allies are directly hitting some of Putin’s closest advisers with sanctions in a move intended to isolate and punish the Kremlin.

Foreign policy analysts warn the latest steps could be the beginning of a deep freeze in U.S.-Russian relations.

“This has the potential to end very badly,” said Richard Fontaine, president of the Center for a New American Security. “I don’t think this means war, but this could spell the beginning of a long period of extreme diplomatic alienation between the West and Russia.”

The tit-for-tat intensified on Monday, as Obama announced sanctions against Russians and Ukrainians deemed responsible for Russia’s incursion into Crimea, including close allies of Putin and former Ukrainian President Viktor Yanukovych.

Obama said that the U.S. would “calibrate our response based on whether Russia chooses to escalate or de-escalate the situation,” and administration officials did not rule out sanctioning Putin directly, an action rarely taken against a foreign head of state.

Putin was unbowed, and quickly issued a decree declaring Crimea a sovereign and independent nation.

He followed that up on Tuesday by signing a treaty that would annex Crimea.

In a speech to both houses of Russia's parliament, he argued the referendum on Crimea's succession was legal and that Russia could not abandon Crimea, an area with long ties to his country.

“We couldn’t leave Crimea in the lurch; otherwise we would be considered traitors,” Putin said according to an interpreter. “[The West says] we are violating norms of international norm. It’s good that they realize international laws still exist. It’s better late than never.”

Gary Berntsen, who served in the CIA Directorate of Operations between 1982 and 2005, said Putin is likely to take Crimea while working covertly to annex other parts of Ukraine.

"The Russians are unlikely to just roll into Ukraine with tanks. They will likely try to subvert the political process in other parts of Ukraine,” he said. "Putin’s made a very bold calculation [over Crimea] and he’s proceeding. He’s assessed that we won’t move against him militarily, and he’s moving ahead.”

John Bellinger III, who was legal adviser at the State Department under former Secretary Condoleezza Rice, said the Kremlin is likely to retaliate against the U.S. by leveling sanctions against American officials.

“I expect that Putin will announce retaliatory sanctions against certain U.S. officials, if not tomorrow, then soon thereafter,” said Bellinger, who currently heads an international law practice. “Putin is likely to be especially incensed by the sanctions against several of his close advisers.”

The Daily Beast reported Monday evening that the Kremlin was preparing sanctions that included Russian travel bans on several U.S. senators.

Obama and Putin have spoken by phone three times since Russia’s military intervention in Crimea, including a marathon 90-minute phone call. The latest conversation occurred on Sunday after the Crimea referendum, a vote the U.S. and allies say is not legitimate.

Obama warned on Monday that additional sanctions could be on the horizon — and White House officials would not rule out bringing down the hammer on Putin.

“We're not going to rule out individuals or rule out actions, except to say that there will be additional costs imposed on Russia, if Russia does not change direction here when it comes to how it's handling the situation in Ukraine,” White House spokesman Jay Carney said.

The sanctions announced Monday target the assets of seven individuals in the Russian government, in addition to four Ukrainian officials, and will prevent any American citizen from doing business with them.

“If they want to transact in dollars, they will be unable to do so,” said an administration official, who added that, in the past, individuals targeted for American sanctions “tend to find great difficulty in accessing financial services elsewhere.”

Fontaine said the U.S. is trying to increase pressure on the Kremlin with the sanctions while also providing an “off-ramp” to de-escalate the situation in Ukraine.

“The problem with that is Putin has shown absolutely no appetite whatsoever for any off-ramp,” Fontaine said.

“The question is, are these sanctions significant enough to impose a cost that he would find painful enough that he would reverse his position,” he added. “I don’t think he’s going to back off only in response to these sanctions. If this is the first of more things to come, then that’s a step in the right direction.”

The White House is coming under pressure from Republicans to turn up the heat on Putin.

Sen. John McCain John Sidney McCainMomentum growing among Republicans for Supreme Court vote before Election Day McConnell urges GOP senators to 'keep your powder dry' on Supreme Court vacancy McSally says current Senate should vote on Trump nominee MORE (R-Ariz.) has criticized the Obama administration for not providing military assistance to Ukraine, and Monday called for admitting Georgia and Montenegro into NATO.

“The crisis in Ukraine calls for a far more significant response from the United States,” McCain said.

Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (Tenn.), the top Republican on the Foreign Relations Committee, pushed Obama to consider direct military assistance to Ukraine.

“So far, the administration’s calibrated actions have failed to affect Vladimir Putin’s decisions, and that has to change,” Corker said Monday.

While the Obama administration has focused on diplomatic efforts, the U.S. military has also bolstered its presence in Eastern Europe to send a message to both Russia and worried allies in Europe.

"Our actions in the region serve to demonstrate our commitment to our collective defense responsibilities and provide reassurance to our NATO allies," Pentagon spokeswoman Eileen Lainez said Monday. "We continue to support the diplomatic approach to the resolution of the crisis in Ukraine.”

So far, about 200 U.S. airmen and an additional 12 F-16s have arrived at Lask Air Base in Poland, according to European Command spokesman Navy Capt. Gregory Hicks. Flight operations were set to start Monday, but were postponed due to inclement weather.

NATO officials don’t expect to see near-term military “stand offs” with Russia, but are planning to bolster Ukrainian forces in the long-term, a NATO official told the Hill.

NATO plans to help Ukrainian forces build capacity via joint exercises, advice and other unspecified things, the official said.

- Rebecca Shabad contributed.

This story was updated at 9:43 a.m.