A plurality of respondents (48%) approved of Obama's handling of the situation in Ukraine, the poll found. That figure was higher than the president's overall job-approval rating, which has hovered in the low 40s.
Russia has sent troops into the Crimean peninsula and encouraged what Obama has called an "illegal" referendum on March 16 that is to decide whether Crimea secedes from Ukraine to become part of Russia.
About 59% of poll respondents said they favored imposing economic sanctions on Russia -- a move that the president put in play last week when he authorized the Treasury secretary to freeze the assets of people found to be involved in subverting Ukraine's democracy or invading its territory.
However, fewer than half, 46%, said they favored providing economic assistance to the Ukrainian government. Secretary of State
Some Republicans, most notably Arizona Sen.
CNN’s poll numbers indicate there is little public appetite for any sort of military involvement in Ukraine, even among Republicans, after a decade of intense engagement in Iraq and Afghanistan.
Overall, 17% of respondents -- including 16% of Republicans -- said they favored airstrikes against Russian troops in Ukraine.
Twelve percent said the Obama administration should send in ground troops -- 16% of Republicans said that was a good idea, compared with 11% of Democrats and independents, respectively.
Most striking, fewer than a quarter of Republicans, Democrats or independents surveyed favored sending weapons and other military supplies to help the Ukrainian government -- and more Democrats than Republicans favored offering economic assistance, 56% to 43%.
As the Republican Party wrestles over its message, those kinds of findings could bolster the presidential aspirations of a candidate such as Kentucky Sen.
At the CPAC gathering, where young libertarians played an important role, Paul handily won a straw poll measuring enthusiasm among core conservatives for possible 2016 presidential contenders.
Paul's speech received one of the most enthusiastic responses at the three-day event but, in a stark contrast with his rivals, he did not mention Russia once.
[Clarification, 9:14 a.m. PDT March 11: An earlier version of this post indicated that some Republicans, including Arizona Sen.