He did not provide additional details.
The top Republican on the Senate Foreign Relations Committee pushed for targeting specific sectors of the Russian economy.
"To me, hitting four of the largest banks there would send shockwaves into the economy. Hitting Gazprom would certainly send shockwaves into the economy," Sen. Bob Corker of Tennessee said, referring to Russia's state gas monopoly.
Corker added that the current sanctions on individuals are "not creating the kind of pain within Russia that will cause Putin to change his behavior."
But Blinked detailed the effects that he said current sanctions have had on Russia: financial markets down 22 percent since the beginning of the year, the ruble at an all-time low, $70 billion in capital moved out of the country.
Blinken said the sanctions are aimed at a compact Putin made with the Russian people to deliver economic growth in exchange for political complacency. The penalties are making fulfillment of his promise difficult for Putin.
"We're already seeing projection for growth going into under 1 percent this year. So that compact is eroding and he has very hard choices to make," Blinken said.
Earlier Sunday, President Barack Obama said in Malaysia that the U.S. would be in a stronger position to deter Putin once Putin sees the world is unified in punishing Russia.
Obama said Russia wasn't abiding by a deal reached to ease tensions.
Blinken made his comments on CNN's "State of the Union," CBS' "Face the Nation" and NBC's "Meet the Press." Corker appeared on CBS.