Republican voters would like to see Rick Santorum or Sen. Marco RubioMarco RubioLongtime GOP incumbent will not seek reelection Overnight Defense: Commander calls North Korea crisis 'worst' he's seen | Trump signs VA order | Dems push Trump to fill national security posts What’s with Trump’s spelling mistakes? MORE (R-Fla.) standing at Mitt Romney's side this fall, a new poll found.

Reuters-Ipsos poll released Thursday found Santorum and Rubio are the top choices among Republican voters to be Romney’s running mate.

Republican voters were presented with a list of 19 names, and a plurality, 18 percent, said Rick Santorum would be the best candidate to fill out the GOP ticket, while 17 percent went for Rubio.

Rubio was by far the most popular candidate with Tea Party supporters, and the only potential vice presidential pick to pull more than 20 percent with any of the groups represented in the poll.

In addition to being from a swing state with a large delegate prize, Romney might find Rubio’s Tea Party support appealing as a running mate, since he has struggled to win over some conservatives. Santorum came in second among Tea Party supporters with 16 percent.

But if Romney hopes to appeal to independents, Rubio performs dismally, pulling only 4 percent of their support. Santorum led among independents at 16 percent, and was followed closely by New Jersey Gov. Chris Christie and former Florida Gov. Jeb Bush (R).

Christie and Bush tied for third among Republicans in the poll, each pulling 13 percent, with former Arkansas Gov. and GOP presidential candidate Mike Huckabee taking 12 percent.

A number of potential VP picks who seemed to be gaining momentum recently barely registered in the poll.

Rep. Paul RyanPaul RyanDems, not trusting Trump, want permanent ObamaCare fix Kudlow: Trump's tax plan 'a home run' Samantha Bee roasts Trump at mock correspondents' dinner MORE (R-Wis.), the author of the House Republican budget, campaigned with Romney in his home state last week but logged only 4 percent in the Reuters-Ipsos poll. Virginia Gov. Bob McDonnell, who appeared with Romney at a campaign stop in his home state on Thursday, didn’t even register in the poll.

Ohio Sen. Rob PortmanRob PortmanTrump talks big on trade, but workers need action Trump tax plan prompts GOP fears about deficit Overnight Regulation: Senators call for 'cost-effective' regs | FCC chief unveils plans to roll back net neutrality MORE, who many believe to be the safest pick, and therefore the likeliest, also failed to register in the poll, finishing behind Indiana Gov. Mitch Daniels, Louisiana Gov. Bobby Jindal and former Minnesota Gov. Tim Pawlenty.

The Reuters-Ipsos poll of 579 Republicans has a 4.7 percent margin of error, the poll of 308 independents has a 6.5 percent margin of error, and the poll of 317 Tea Party supporters has a 6.4 percent margin of error.