Russian President Vladimir Putin was not on the list of 11 Russian and Ukrainian names sanctioned by the U.S. government Monday, but the White House would not rule out the possibility when pressed about getting more aggressive with the Kremlin.

“We're not going to rule out individuals or rule out actions,” White House press secretary Jay Carney said when asked about sanctions against Putin.

President Obama earlier Monday announced sanctions against seven senior Russian officials and four others associated with separatist movement in Ukraine. For its part, the European Union also said it was sanctioning 21 officials.

The White House is hoping that Putin will draw down his forces in Ukraine in the face of economic headwinds in Russia.

Yet, Putin on Tuesday is expected to endorse the Russian annexation of Crimea.

Obama’s top spokesman would not say whether such a development would initiate sanctions against the Russian president.

However, Obama’s critics accused the president of not doing enough to counter Putin, who views Ukraine as an extension of Russian power and influence.

“This president's response -- I don't know how it could have been weaker, besides doing nothing," Sen. John McCain, R-Ariz., told MSNBC's Andrea Mitchell.

"I don’t know when the president and his advisers are going to wake up to what Putin is really all about," he added. "We've got to start with a fundamental reassessment of our relationship with him."