Most Democrats say the sanctions are OK, while a majority of Republicans finds them too weak.
"We're supposed to be a country that helps smaller countries in need," said Christopher Ashby, 29, a Republican in Albemarle, N.C., who wants a more powerful response. "Ukraine at this time is definitely in need."
Ashby, a stay-at-home dad caring for three young daughters, said, "When I look at Obama, I see my 5-year-old daughter looking at something that just happened and saying 'What do I do?'"
Overall disapproval of the job Obama is doing ticked up to 59 percent — a record high for his presidency — in the poll released Wednesday. His 41 percent approval rating is a sobering number for fellow Democrats running in this fall's House and Senate elections.
Americans are now divided over which party they would rather see in control of Congress. Democrats held a slight edge over Republicans in the January AP-GfK poll.
Obama gets lowest marks for his handling of the federal budget, immigration and the economy. Support for Obama's education policies, which had been a strong point, dipped into negative territory this month, too.
Republicans have long criticized the president as too weak in asserting American power abroad. Yet until now, foreign policy hasn't been a drag on Obama's second term: Americans were about as likely to endorse his actions as to disapprove.
Now he's hit a new low on international relations — just 40 percent approval.
Majorities say they dislike Obama's handling of the Ukraine situation (57 percent) and his interactions with Russia (54 percent).
Almost half of those polled say they support imposing tougher sanctions if Russia pushes into new regions or other countries; only 14 percent are opposed. That backs up threats from Obama and Western allies to target Russia's economy with damaging sanctions if President Vladimir Putin goes further.
About a third of those surveyed said they oppose giving monetary aid to nations targeted by Russia. Only about 20 percent approve of financial support, while the biggest share is neutral. This week Congress is considering $1 billion in loan guarantees for Ukraine sought by Obama.
The idea of lending any type of military support to Ukraine is unpopular, the poll says. Obama has said there are no plans to use military force to dislodge Russia from the Crimean Peninsula.
Richard Johnson, a politically independent retiree in Redmond, Wash., said the United States shouldn't have gotten involved at all, especially since many Crimean residents favor Russia.
"They're protesting in both directions, right?" Johnson said. "So I just feel like we've got enough problems here at home, why are we looking for more trouble?"
Johnson, pausing from wiring work on his do-it-yourself kitchen remodel, said he still supports Obama nevertheless.