By Thomas Ferraro

WASHINGTON (Reuters) - Republican U.S. Senator Ted Cruz of Texas, a Tea Party favorite seen as a potential 2016 presidential contender, on Thursday put Democrat Hillary Clinton's chances of winning the White House at 40 percent.

"The media thinks she is unstoppable, but they also thought she was unstoppable in the 2008 Democratic primary," which Barack Obama won en route to the White House, Cruz said of the former secretary of state and wife of two-term U.S. President Bill Clinton.

Cruz said Clinton would be vulnerable in a general election for a number of reasons, including what he called Obama's failed economy and the traditional shift in voter preference.

"There is a natural pendulum in politics," Cruz said, with the public often ready to turn to the other party after one party has held the White House for eight years.

Obama is in his second, four-year term.

Cruz, who spoke at a Politico Playbook Breakfast, was pressed by moderator Mike Allen on whether he planned to run for the presidency.

"It's premature," the Texas Republican said.

But Cruz said Republicans would stand a better chance of capturing the White House if they put forward a conservative, rather than moderate, candidate.

"Let's look at the last 40 years," Cruz said. "Every single time Republicans have nominated a presidential candidate who ran as a strong conservative, we won. And every time we have nominated a candidate who ran as an establishment moderate, we lost."

"What I find to be astonishing is that the D.C. political consultants look at that record and say, 'In 2016, we need another establishment moderate," Cruz said.

As a freshman senator, Cruz has earned a reputation as an outspoken conservative who has won the admiration of the anti big government Tea Party movement. He has also accused Senate Republican leadership of being too willing to compromise.

Last year, he bucked leadership and pushed a strategy to deny funding to President Barack Obama's healthcare plan that resulted in a 16-day government shutdown. The strategy fueled ill will toward Cruz among many Senate Republicans when the shutdown provoked a public backlash against their party.

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More recently, Cruz demanded that the Senate come up with 60 votes - rather than 51 - to advance a bill raising the debt ceiling. That put a handful of Republicans, including Senate Minority leader Mitch McConnell of Kentucky, in the awkward position of having to vote to allow the debt ceiling bill to move forward even though they opposed it.

Tea Party-backed candidate Matt Bevin, who is challenging McConnell in a primary election race in Kentucky, has criticized him over the vote, saying he caved in to Democrats.

Cruz said he would stay out of the primary contests.

"I'm not supporting any of the senators in my party or their opponents," he said. "I'm leaving it to the grass roots to make their decision."

(Reporting By Thomas Ferraro; editing by Gunna Dickson)