WASHINGTON (CBS DC) — Sen. Ted Cruz, R-Texas, dismissed speculation that he would contest Sen. Mitch McConnell for the Republican Senate majority position, despite very differing views between the two GOP senators on the Affordable Care Act, immigration and threats of another government shutdown.

When asked by CBS News if there would be a challenge to the next probable Senate Majority Leader Mitch McConnell, Cruz said he was not aware of a challenger to the Kentucky senator re-elected to his sixth term on Tuesday.

“Well I don’t think anyone has declared their intention to run and that’ll be a decision for the conference next week and we’ll see,” said Cruz, adding that “under no circumstances” would he choose to run for the position.

“My practice has been not to second-guess leadership decisions,” said Cruz. “I realize that folks like to focus on interpersonal jockeying between politicians in Washington…I think Republicans should do everything humanly possible to stop Obamacare,” said Cruz. “I think we need to start by using reconciliation to pass legislation repealing Obamacare.”

Cruz said that should Obama veto such pushes by Congress then specific actions would be taken to stop individual issues including insurance company bailouts or insurance policy cancellations.

But the Texas Tea Party darling owes much of his heightened national profile to bucking leadership in his own party in addition to his spearheading of the October 2013 government shutdown – a move largely opposed by GOP leadership.

Cruz refused to pledge support for McConnell ahead of the Kentucky senator’s Tuesday victory, exposing some of the stark differences between the two Republicans and leading many to suggest that the Texas conservative may push for the position.

Speaking with Time Magazine this week, McConnell said “there is no possibility of a government shutdown,” adding, “I’m the guy that gets us out of government shutdowns.”

McConnell also said that a full repeal of Obamacare is not on his mind, instead favoring a rejection of specific elements of the Affordable Care Act through the appropriation process.

Cruz told CBS News that he did not play a role in shutting down the government last October in order to block Obamacare, saying instead that it was Senate Majority Leader Harry Reid and President Barack Obama who shut down the government.

McConnell declined to comment on his stance regarding immigration reform, which comes just two weeks after Cruz penned a USA Today opinion piece that called for a hard line on immigrants.

Asked about reaching out to Cruz and other Republican presidential hopefuls, McConnell took a moderate stance.

“Look, we have a big party,” said McConnell. “Everybody from [Maine Senator] Susan Collins to Ted Cruz. There are lots of different points of view. Bringing them together, that’s my job and I work on it every week.”