We didn't declare war on North Korea, but killed about 500,000 people. We didn't declare war on Vietnam, but killed about 600,000 people. We didn't declare war on Nicaragua, Panama, Grenada, Yugoslavia, Kosovo... we didn't declare war on Iraq, but we killed 35k the first go 'round and another 100k or so the second time. We don't declare war on anything real anymore (just poverty or drugs...).
Suddenly with Obama in the White House this is an issue?
And every other President has utilized extra judicial killings, including airstrikes, cruise missile attacks, and drone strikes when they became available. Again, suddenly this is an issue?
I agree with your basic premise, we would be more than hostile if Russia decided some Israeli was a terrorist and dropped a bomb on him in Tel Aviv. However, I disagree that this is somehow an Obama issue as opposed to simply an American issue.