Ukraine is much more important to Russia than to the U.S. It borders Russia, was part of the Soviet Union, and much of what is now Ukraine, including Kiev, has been part of Russia from time to time for as long as the United States has existed. Ukraine’s importance to the U. S. is, however, more academic. It is reasonable to assume that as long as it is economically able Russia will counter any increase in Ukraine’s military capacity and activity in eastern Ukraine (the part bordering Russia) with equal or greater military force. If we increase our support and Ukraine elevates its military activities in the east, so will Russia. The Russian economy is suffering from years of exploitation by Putin and his friends as well as inadequate investment and is now suffering from the sharp fall in the prices of its primary exports– oil and gas. Russia will presumably only stop matching escalations from the West when it is no longer economically able to do so. Do we have a national security interest in escalating that far?
Our interest in Ukraine is humanitarian– not military out of a concern for our own security. We would like to see the people of every country enjoy the freedom and prosperity that we have. Moreover, most of us have long believed that healthy, prosperous, well-governed countries make better neighbors and a more peaceful and prosperous world. So it serves that interest and our humanitarian natures to encourage and financially support the new Ukrainian government’s efforts to reduce the corruption their country has long suffered from. Military aid is an entirely different matter.
Both we and Ukraine’s government in Kiev must accept and come to reasonable terms with Russia’s dominance in the area and its determination to remain in Eastern Ukraine as it has in South Ossetia and Abkhazia. The alternative, which would likely follow the injection of western arms into the conflict, would be a continued escalation of fighting with unknown consequences and an unknown end point. We don’t like to give in, and wouldn’t and shouldn’t whenever our national security is truly at stake, but this is not our war. What, after all, did our “victory” in Iraq (one of the most insane and ill-advised wars we have ever launched) gain us? ISIS!!
Let’s help Ukraine financially, which it desperately needs, as long as its government continues to seriously fight the corruption that has characterized it for so long (easier said than done). Ukrainian offensives in “rebel”/Russian dominated areas of the East are futile and we should not encourage them by providing the weapons that make them possible. Freeze the status quo until Russia comes to its senses (which we should encourage in every possible way) or collapses economically (which we should not hope for).
Warren's space 
The matter is greater than “do we have a vested interest in Ukraine,” my friend. WE, as the freedom fighting country and the hope of the free world, must engage the enemies of freedom and democracy together with other NATO countries when we can. We cannot allow another Germany type infiltration of evil into sovereign countries by any country.
The fact that the United States is a founding country of both NATO and the United Nations, and that Russia has intentionally violated UN accords as well as international law makes this a fight for every democratic country around the world. If Russia and Putin are not stopped in Ukraine, what country is next?
As a consultant or the expansion of the European Union and the gathering of all former Soviet states into the European Union and NATO, it makes sense to provide protection, economic assistance, and military support through NATO- including funding of weapons purchases – which we have already done by the way. We did the same for Afghanistan when Russia invaded there. (Charlie’s War).
As the consultant that advised the EU and the US to impose sanctions to begin with, the only sanctions that have yet to be imposed are “dead bank letters” under the Patriot Act. This would literally crush Russia’s economy in months. While the present sanctions are slowly curbing Russian military spending, Putin and his cronies continue to threaten nuclear war- a truly desperate move indeed.
Yes, we have a humanitarian objective, but in for a penny, in for a pound. The EU wants Ukraine to become a member. As an ally of the EU, the threats of war by Russia against any country must not be permitted by any means. Russia is in a siege mentality. The ruble is dying slowly. Oil prices are only going up due to a reduction in producing wells and wells being shut down to stabilize the price. Saudi Arabia cooperated with the US to open the oil floodgates wide to reduce the price to hurt the economy of Iran as well as Russia (for the USA).
Should we openly enter a war with Russia? Probably not, but we are already in an economic and propaganda war with Russia as I write this. Tyranny in any form must be crushed under the feet of democratic citizens around the world. Russia will not continue to supply eastern Ukraine rebels for long as once NATO gets off of the fence, Russia troops will gladly leave Ukraine.