A CNN/ORC International survey asked Republicans and Republican-leaning independents to choose between eight names who could be among the dozens of potential running mates the Romney campaign might be considering for the vice presidential slot.
Rice topped the list with 26 percent of the participants choosing her as the best possible vice presidential nominee for Romney.
Rick Santorum, a Romney rival who only dropped out of the race earlier this month, came in second place with 21 percent of the participants choosing him as Romney's running mate. Sen. Marco Rubio and New Jersey's governor, Chris Christie, tied at 14 percent in the CNN/ORC poll.
CNN's Polling Director Keating Holland said, "Name recognition is the key. Rice and Santorum are best known and they top the overall wish list."
Christie led the pack in a Quinnipiac University poll, with 31 percent of the respondents calling him a good choice, compared to 18 percent who said he would be a bad choice. Rubio was also given a nod at 24 percent, with 14 percent not in favor. Rep. Paul Ryan was also viewed as a good choice by 23 percent, with 17 percent saying he would not be a good choice.
Rubio, speaking on Thursday, said he would say no if Romney asked him to join the ticket, stating, "Sen. Rob Portman would be a phenomenal choice for vice president, that's where I would encourage him to look, because I'm enjoying my service in the Senate," according to MSNBC.
Much was made of the tea party favorite's slip of the tongue when he said, "If I do a good job as vice president," instead of senator.
Rice, serving as secretary of State under the Bush administration, has also said she would not be interested in being a presidential running mate, according to USA Today.
On April 16, Romney tapped adviser Beth Myers to lead the search for his vice presidential running mate, according to The Washington Post.