Almost everything that Obama administration has officially said on defense/military aid to Ukraine appears to have been vague generalities. When it comes to details, it seems the Obama era PR on Ukraine was done largely with [semi-]sanctioned officials talking to the press, sometimes on condition of anonymity, e.g. NPR reported on Feb 2, 2015:
President Barack Obama is reconsidering sending lethal assistance to Ukraine, a senior administration official said Monday, but continues to have concerns about the effectiveness of that step and the risks of a proxy war between the U.S. and Russia.
The official said Obama is specifically concerned about the besieged Ukrainian military’s capacity for using high-powered, American-supplied weaponry. The president has also argued that no amount of arming the Ukrainians would put them on par with Russia’s military prowess.
The official requested anonymity to speak because the person was not authorized to talk publicly about internal deliberations.
The U.S. accuses Russia of supplying the pro-Kremlin separatists that are stirring instability in eastern Ukraine. The U.S. has limited its supplies to the Ukrainian military to non-lethal aid, such as gas masks and radar technology to detect incoming fire.
However, some administration officials have been pressing Obama for months to step up that assistance. With violence in eastern Ukraine on the rise in recent weeks, the official said Obama is willing to take a fresh look at supplying Ukraine with lethal aid, along with other options for calming tensions.
The non-lethal aid still involved (lightly) armored vehicles and counter-mortar radar if I recall correctly. They've only got counter-mortar radar, not the longer range counter-artillery one Ukraine had hoped for because the US apparently was afraid back then than with the longer-range radar Ukraine might fire at batteries on Russian soil, as the BBC reported on Feb 5, 2015:
Modern heavy armour gave the rebels the advantage in fighting at Donetsk airport recently, Reuben Johnson of Jane's Defence told the BBC. [...]
Ukraine has asked the US for Javelin anti-tank missiles and hi-tech radar that locates heavy artillery, he said. [...]
"About 70% of Ukrainian anti-tank missiles are old or even expired. But almost all the Russian armour is reactive - that means boxes of explosives cover the tank, so when a missile hits a box it blows up the missile without harming the tank."
Last year Ukraine asked the US for counter-battery radars, which can show the path of incoming projectiles, he said.
Such tracking radars enable troops to pinpoint an artillery or mortar unit, which can then be targeted.
"They got counter-mortar radar - but its range is shorter, and it didn't work," Mr Johnson said.
Counter-artillery radar was not supplied apparently because the US government feared that Ukraine might then target artillery pieces firing from Russian soil, he said.
Nevertheless, the counter-mortar radar was quite useful as some experts quoted by DefenseNews say:
Some of the early nonlethal aid was useful. After Ukraine received 20 Lockheed Martin AN/TPQ-53 radar systems that track incoming mortar and short-range artillery fire in 2015, the casualty rate for units equipped with those system went from 47 percent to about 18 percent, [Col. Andrii] Ordynovych, [Ukraine’s military attache in Washington] said.
Likewise LA Times reported in March 2015,
The United States will provide Ukrainian forces fighting Russia-backed separatists $75 million in nonlethal equipment, including small reconnaissance drones, radios and military ambulances, a senior administration official said.
President Obama has also approved the transfer of 30 armored Humvees and up to 200 unarmored Humvees under a separate authority, said the official, who was not authorized to speak publicly on the matter and requested anonymity. [...]
Thus far, the U.S. has given only nonlethal aid to Ukraine’s military, including medicine, night-vision goggles and armored vests since the conflict erupted. As many as 300 American troops are also to be sent to the Lviv region on Ukraine’s western border, far from the conflict zone, to train Ukrainian soldiers. [...]
The package includes counter-mortar radars for warning and protection against mortar and artillery fire and night-vision devices. It also includes small remote-controlled Raven drones, made by AeroVironment Inc. in Simi Valley, that are thrown into the air by soldiers and provide a bird’s-eye view of what’s happening over a ridge or around a bend.
I did find a statement of Obama himself from August 2014, as paraphrased and partially quoted by RFERL:
U.S. President Barack Obama says Ukraine does not need additional military assistance to help fight pro-Russian separatists but an invasion by Russia would raise "a different set of questions."
Obama's comments came after NATO said on August 6 that Moscow had increased its forces along the border with eastern Ukraine to some 20,000 troops.
Obama said Ukraine is fighting separatists "who can't match the Ukrainian Army."
Ukrainian officials have urged Washington to provide lethal aid to Kyiv.
I'm not sure if Obama himself made more nuanced statements after that.
NYT reported in June 2015:
With the peace process stalled and violence escalating in Ukraine, a bipartisan coalition in Congress is defying President Obama and European allies by pressing the administration to provide weapons to the embattled nation. [...]
So far, the Obama administration has refused to provide lethal aid, fearing that it would only escalate the bloodshed and give President Vladimir V. Putin of Russia a pretext for further incursions. [...]
Legislation to authorize lethal military aid for Ukraine has gone to the White House before, but Mr. Obama has not acted on it. And while this bill authorizes the weapons it cannot compel the administration to send them. The measure is largely meant to put renewed pressure on the White House. [...]
But in the latest sign of the reluctance by the White House, Samantha Power, the United States ambassador to the United Nations, gave a speech on Thursday in Kiev, the Ukrainian capital, in which she excoriated Russia but did not mention sending offensive weapons as a possibility.
There's no quote from Obama himself in that later piece though.
There's (paywalled) interview with Obama from 2016, that was paraphrased as
As regards the two-year-old conflict between Ukraine and Russia, the president said Ukraine is a core interest for Moscow, in a way that it is not for the United States. He noted that, since Ukraine does not belong to NATO, it is vulnerable to Russian military domination, and that “we have to be very clear about what our core interests are and what we are willing to go to war for.”
The interview is actually quote long but does not get into any specifics on aid to Ukraine. Obama does spend quite some time rejecting the "crazy man" theory of Nixon as he attributed it.
The site of the Obama White House has a page on aid to Ukraine, last updated in June 2016. It's also rather devoid of specifics though, when it comes to military/defense aid to Ukraine; it mentions
These initiatives and new commitments are part of more than $1.3 billion in foreign assistance the U.S. government has committed to Ukraine since 2014 to advance reforms, strengthen democratic institutions and civil society, stimulate economic growth, strengthen its defenses, and help Ukraine more safely monitor and secure its borders and defend its territorial integrity.
Nothing more specific than that generic "strengthen its defenses" and "safely monitor and secure its borders and defend its territorial integrity" in there.
