The chairman of the Republican National Committee said Monday that the key to winning over Hispanic voters this year is to convince them that President Obama has failed to strengthen their economic prospects — not by pandering to them with promises of a path to citizenship for illegal immigrants.

Speaking to reporters in a conference call, Reince Priebus described the economy as an “emotional” issue for Hispanic voters, the nation’s fastest-growing voting bloc, and said that Mr. Obama has failed to deliver the kind of immigration reform that he touted during the 2008 presidential campaign.

“The president delivered a fat goose egg on the issue,” he said, specifically referring to the president’s failure to overhaul federal immigration laws or offer a pathway to citizenship for those in the country illegally. “He is the person who traveled and campaigned on the basis of [a citizenship] pathway and delivered nothing. I mean, once someone lies to you multiple times, … why would you believe him again?”

The conference call comes as the national party prepares for the stretch-run of the presidential election, which will kick into high gear when thousands gathered in Tampa for the Republican National Convention in Tampa, Fla. in late August.

While the White House is the big prize up for grabs, 33 Senate seats and all 435 seats in the House — including several races where Hispanic voters could make or break a campaign — will be on the ballot...