Sen. Ted Cruz, R-Texas, is keeping an open mind about Senate Intelligence Committee chair Dianne Feinstein's accusation that the CIA hacked into her staff's computers, but he said the alleged behavior is "consistent with a pattern" of President Obama abusing executive power.

Cruz wouldn't say if CIA Director John Brennan should lose his job. "I think we should wait to discover what the facts are, but for the executive branch to spy on and hack into the computers of the United States Senate is an extraordinary violation of the respect that each constitutional branch owes the other, and so, if that is indeed what happen[ed], there should be serious consequences," he told the Washington Examiner outside the Senate chamber.

The fight between Feinstein and the CIA pertains to a Senate report on waterboarding during former President George W. Bush's time in office. McClatchy reported Friday that the CIA had learned of congressional staffers removing secret documents from agency headquarters by monitoring Senate computers.

"The CIA just went and searched the committee's computers," Feinstein, a California Democrat, said Tuesday on the Senate floor. "I have grave concerns that the CIA's search may well have violated the separation of powers principles embodied by the United States Constitution, including the speech and debate clause."

Brennan denied that his agency hacked the computers. "The CIA was in no way spying on [the committee] or the Senate," he told NBC after Feinstein made the accusation.

Cruz said Congress needs to learn the facts of the case. "I would note it is consistent with a pattern of the Obama administration of disregarding the constitutional liberties of the citizenry and disrespecting the constitutional role of the United States Congress," he said.

Though he and Feinstein agree on the impropriety of such searches, Cruz argued that Democrats have enabled Obama's disrespect of congressional prerogatives. Democrats, he noted, applauded during the 2014 State of the Union speech when Obama pledged to act without Congress. Also, Cruz mentioned, Senate Democrats supported so-called 'recess appointments,' which were made when the Senate was technically in session.

"The absence of Democrats standing up to the president on those unconstitutional recess appointments only encourages future abuse of executive power," Cruz said.