Former Secretary of State Condoleezza Rice on Sunday said that immigration reform would be a pivotal issue for Republicans, who needed to prove their party had “broad appeal.”

"I think immigration is really the big issue, frankly. We sent some pretty bad signals around immigration," said Rice, as she made her debut as a CBS News contributor on “Face the Nation.”

In a panel discussion, Rice said the Republican Party needed to shift its messaging on immigration and said voters would be watching the upcoming debate on comprehensive immigration reform in Congress.

"The Republican Party certainly has to stop turning off large segments of the population. I've said it's not a strategy to keeping hoping that parts of the population don't turn out. You've got to simply broaden," Rice said. "The Republican Party has to demonstrate that it has broad appeal."

Rice also praised Sen. Marco RubioMarco Antonio RubioRepublicans think Trump is losing trade war The Hill's 12:30 Report — Sponsored by Delta Air Lines — Trump meets South Korean leader as questions linger about summit with North Senators demand answers on Trump’s ZTE deal MORE (R-Fla.) for leading the call for immigration reform among Republicans in the Senate.

Rice also said that President Obama, who began his second term Sunday, would need to remain focused on the nation’s economy.

"The first challenge is to do something about the American economy, because I do think that our international leadership has suffered both from the perception that America can't get its act together on entitlements and the deficit and so forth, and from the reality that without a stronger economy there are just some things we cannot do," Rice said.

Rice is the first African-American woman to serve as secretary of State. She formerly served as President George W. Bush's national security adviser and has faced criticism for the Bush administration's handling of the Iraq war.

Rice was one of the top speakers at the Republican National Convention this summer. She is currently a fellow at Stanford University's Hoover Institution and a professor at Stanford's Graduate School of Business.

On Sunday, "Face the Nation" host Bob Schieffer announced Rice's new role as a contributor with CBS News.