After President Obama suggested this week that the U.S. might impose further sanctions against Russia for its latest incursion into Ukraine, Democrats still aren't fully bought in to the idea.

"I'm not sure they will work," Senate Intelligence Committee Chairwoman Dianne Feinstein said on NBC's "Meet The Press" on Sunday. "I'm not sure that shakes the people that much, and it's the people that have to be spoken to."

Feinstein contended that, for as long as Russians support President Vladimir Putin, sanctions would have a very limited impact.

"I think if Russians follow him, and up to date they are following him, the Russians are very brave and very long-suffering and they will tough out any economic difficulty," Feinstein said.

Feinstein proposed staging direct talks with Putin.

The U.S. already imposed a first round of sanctions on Russia earlier this year, which the president has called "effective."