Cruz: Hillary will win if another Romney-type runs

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Sen. Ted Cruz, a tea party favorite and possible presidential contender, told CNBC on Thursday the only way the GOP can win the White House in 2016 is to run a strong conservative candidate.

"We need to learn from history," the Texas Republican said in a "Squawk Box" interview. "If Republicans run another candidate in the mold of a Bob Dole or a John McCain or a Mitt Romney ... we will end up with the same result, which is millions of people will stay home on Election Day."

"If we run another candidate like that," he continued, "Hillary Clinton will be the next president."

In political circles, many believe the former secretary of State will again seek the Democratic nomination for president, though she has not said either way yet. Hillary Clinton lost the nomination in 2008 to Barack Obama.

Supports states' rights on gay marriage

On social issues, Cruz said he supports the rights of the states to decide whether to allow same-sex marriage even though he personally believes in marriage between one man and one woman.

He appeared on CNBC ahead of next week's midterm election and as news was breaking Thursday morning about Apple CEO Tim Cook announcing he's gay.

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"I support marriage between one man and one woman," Cruz said. "And I support the Constitution letting each state decide each marriage law consistent with the values of their citizens."

"One of the problems of the 'big government left' is they want everything to be a one-size-fits-all solution from Washington," he said.

In a separate "Squawk Box" interview Thursday, liberal Democrat Barney Frank, retired openly-gay congressman from Massachusetts, praised Cruz for those comments.

Read MoreBarney Frank in praise of ... Ted Cruz?

'Very optimistic' about midterm election

Cruz, known for bucking the Republican establishment, is not up for re-election until 2018. But the freshman senator from Texas said he's been crisscrossing the nation in support of conservative candidates in the runup to Tuesday's voting.

"I am very optimistic," he said. "I think Republicans are going to retake the Senate. We're going to retire Harry Reid." The Senator Majority Leader Reid, a Democrat from Nevada, has been a thorn in the GOP's side for years.

In a USA Today op-ed earlier this month, Cruz laid out an agenda for 2015, assuming that Republicans would retain the House and gain control of the Senate. He said Congress should work to jumpstart the economy, safeguard constitutional liberties and strengthen national security. He also advocated repealing Obamacare, auditing the Federal Reserve, and getting rid of the federal education Common Core standards.

He echoed those economic themes in Thursday's CNBC interview. "On Wall Street, things are booming. But for working men and women, life has gotten harder and harder and harder. What we're doing under the Obama economy isn't working."