Mari Carmen Aponte, who was nominated by Obama in December, withdrew her nomination to another diplomatic post in the Clinton era following questions about her past relationship with someone who had apparently caught the attention of the FBI.
"Serious concerns about this nominee arose when she was nominated for a different position during the Clinton administration," DeMint said in a written statement to FoxNews.com. "I have asked the committee for additional time to review these matters. So far we have not received all of the information we have requested."
In 1998, President Clinton's nomination of Aponte for ambassador to the Dominican Republic fizzled after the foreign relations panel questioned her over her past relationship to Roberto Tamayo, who had raised concern at the FBI over "possible ties to the Cuban government" and "repeated trips there," one former official with knowledge of that nomination told FoxNews.com.
Aponte came under scrutiny by the committee after revelations that she attended a party at the Cuban mission to the United Nations in New York City, the former official said.
According to reports at the time, a former Cuban intelligence agent also told a Spanish-language newspaper in Miami in 1993 that Cuban intelligence was trying to recruit her through her boyfriend.
By the time Clinton nominated her, that relationship had ended -- the former official said the Senate committee had no evidence of any such recruitment either. But the source said the committee was ultimately concerned about her relationship with Tamayo, and whether it could be exploited by the Cuban government.
The Miami Herald reported in 1999 that the FBI had cleared Aponte of being targeted in any recruitment scheme. The Washington Times quoted a former FBI agent at the time as saying Tamayo was actually a valuable source of information for the FBI.
The White House defended Aponte when her nomination was announced in December.
"As has been previously reported, the FBI fully investigated this issue in 1999, and Ms. Aponte received a thorough background check by diplomatic security as part of the nomination process this time around," White House spokesman Tommy Vietor said in an e-mail to FoxNews.com.
"Had there been any doubt, the president would not have nominated Ms. Aponte to this position," he said.
But the former official with knowledge of the nomination said Tamayo was probably not an FBI "mole," and his contact with the agency didn't mean he was innocuous.
Aponte has been a prolific contributor to Democrats, including Secretary of State Hillary Clinton when she was running for Senate, and others. The attorney has an extensive legal background, having served as president of the Hispanic National Bar Association, as well as on the board of the National Council of La Raza and the Puerto Rican Legal Defense and Education Fund. She was born in Puerto Rico.
FoxNews.com's Stephen Clark and Judson Berger contributed to this report.