Today, in an address to the United State nation he emphasized that Putin has much larger ambitions than Ukraine. Biden stated that Putin wants to reestablish the former Soviet Union. Hence, I don't doubt that Putin wants reinvent the Soviet Union.
Biden confirmed that the US will not deploy American troops to either Ukraine or any other US ally but he vowed to defend “every inch” of NATO territory.
Putin might have such goal, but it would be very difficult to achieve. I don't think Russia has the military might except they are assisted by their allies like China.
https://www.timesofisrael.com/liveblog_entry/biden-putin-is-the-aggressor-and-will-pay-a-severe-price-for-invading-ukraine/
What Biden is saying is right but without deploying troops how he is going to defend NATO territory? All the NATO members in EU is US ally. What i think is Putin is trying to bring all the focused of NATO in Ukraine as a diversion and then attack some other NATO countries to involve NATO to this war. Only capturing Ukraine is too costly for Russia and hard sanction could force Putin to take any hard decision.