"Not a single issue will define any party. The issue of immigration should not be the one thing that defines the Republican Party. But the system is broken," she said. "We have to do it together with Democrats."
Gillespie and Martinez both stressed that Hispanic voters are not single-issue immigration voters, saying that the party must earn their trust on issues like education and the economy as well. Martinez herself has sparked controversy with her effort to revoke a state law that provided driver's licenses to undocumented immigrants.
But addressing immigration reform that includes some type of relief for the undocumented population at the federal level could "make clear that we welcome people into this country who come here legally," Gillespie said.
Republicans have actually done a good job of churning out prominent Latino elected officials during the past several elections. In addition to Rubio, Sandoval, and Martinez, the GOP now can boast more Hispanic senators than Democrats thanks to the election of Ted Cruz in Texas. Several Hispanic congressmen such as Raúl Labrador (Idaho) have also made their mark. But that hasn't changed their difficulty in appealing to Latino voters.
Martinez, the first Latina governor in the nation's history, insisted that continuing those efforts could eventually breed greater success in attracting minority voters. RSLC officials would not say their targets for recruitment or fundraising for the 2014 election cycle.
"The way for the party to grow again is to elect more Hispanics and more women at the local level," she said.
Hispanic voters, she said, can see through "insincere candidates" whose tone is "not respectful."
"If we are careful about our tone and really listen," she said, "I think the Republicans will do a much better job of recruiting good candidates."