Piggybacking on what House leaders have done, Cruz said the first order of business should be a series of hearings on President Obama, “looking at the abuse of power, the executive abuse, the regulatory abuse, the lawlessness that sadly has pervaded this administration.”

Cruz also would like the Senate to be as aggressive in trying to repeal the Affordable Care Act as the House, which has voted more than 50 times to get rid of the law.

Republicans should “pursue every means possible to repeal Obamacare,” Cruz said, including forcing a vote through parliamentary procedures that would get around a possible filibuster by Democrats. If that leads to a veto by Obama, Cruz said, Republicans should then vote on provisions of the health law “one at a time.”

And when asked whether he would back Sen. Mitch McConnell of Kentucky for Republican leader, Cruz would not pledge his support — an indication that there are limits to how much of a partner he’s willing to be.