The Kentucky Republican said the U.S. should do "a lot less spying on Americans."
The delay will make getting a bill done this week a heavy lift.
Another 29 percent think the United States needs to take a firm stand.
The margin was narrow, with 43 percent disapproving and 42 percent approving.
It would have been the first face-to-face with Putin since Russian troops entered Crimea.
The House on Tuesday is expected to formally condemn Russia for its military action in the Crimean peninsula in Ukraine, less than a week after passing a bill giving financial aid to Ukraine.
Biden will instead attend meetings with Ukraine's prime minister.
President Nicolás Maduro says the U.S. "aims to generate a false image of war."
The two leaders agreed on the importance of sovereignty in Ukraine, the White House said.
He said Russia has clearly crossed a line in Ukraine.