Kentucky Sen. Rand Paul tied with establishment favorite Jeb Bush and surpassed former business executive Carly Fiorina in separate polls released this week. But he is still fielding questions about a potential departure from the Republican presidential field.

Appearing Saturday morning on CNN's "Smerconish," the Kentucky senator was asked to respond to speculations that he may not survive until the earliest nominating contest on Feb. 1 in Iowa.

"We're not getting out until someone votes," Paul told host Michael Smerconish.

"In fact, we think our fortunes are actually improving," he added.

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The libertarian-leaning senator recently completed a tour to nine different college campuses in the Hawkeye State and climbed to fifth place nationally in a CNN/ORC poll released Tuesday, putting him ahead of Fiorina and Texas Sen. Ted Cruz. And in a previous interview with the Washington Examiner, he emphasized the confidence he has in his campaign's ground operation in the earliest voting state.

"One of the interesting and unusual numbers is about 120,000 people caucus in Iowa and there's actually about 120,000 college students in Iowa," Paul told the Examiner. "Nobody thinks we can get all 120,000 out, but our goal is 10,000 and that's about 10 percent of the college population."

One thing voters can expect Paul not to do in early voting states is bring his father, former Texas congressman and 2012 presidential candidate Ron Paul, to campaign on his behalf.

"I'm a great admirer of my dad and think he was one of the greatest people to serve in office, but the race ultimately has to be about the people running," Paul told CNN.

Paul, who is eighth in the latest Washington Examiner presidential power rankings, released a new book this week titled "Our Presidents & Their Prayers: Proclamation of Faith by America's Leaders."