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“Conservatives are just getting to know them,” Mr. Cardenas said of some of the candidates. “None of them have been under the bright lights of the national media in a presidential election. This will give a better sense of how significant their support is at this time.”

The slate of candidates also includes Sens. John Thune of South Dakota, Kelly Ayotte of New Hampshire and Tim Scott of South Carolina.

There are a pair former vice presidential nominees from 2008 and 2012 — former Alaska Gov. Sarah Palin and Rep. Paul Ryan of Wisconsin — and a trio of former presidential candidates who are considering taking another chance at the nation’s top office: former Sen. Rick Santorum of Pennsylvania, Texas Gov. Rick Perry and former Arkansas Gov. Mike Huckabee.

Nikki Haley of South Carolina, Bobby Jindal of Louisiana and Susana Martinez of New Mexico are among the 10 governors who made the cut.

Also on the ballot are famed neurosurgeon Ben Carson, New York real estate mogul Donald Trump, and former Virginia Gov. Bob McDonnell, who is fighting federal corruption charges.

Mr. Paul won the poll last year, and Mr. Rubio came in a close second.

Mr. Paul will have the chance to join his father, former Rep. Ron Paul of Texas, along with Ronald Reagan, Jack Kemp and Mitt Romney, as the only people to have won the poll more than once.

Mr. Romney has won the straw poll four times, while Mr. Reagan and Mr. Kemp each walked away the victor on three occasions.