Farenthold was first elected to the House in 2010, defeating a 14-term Democratic incumbent in a district that was 70 percent Hispanic and bordered Mexico. The race was close—within about 800 votes—but Farenthold appealed to white and Hispanic Democrats alike by arguing that their party had moved too far to the left on issues like abortion and health care. After redistricting, he’s in a much safer Republican district, but 49 percent of his constituents are Hispanic. Farenthold, echoing a common Republican talking point, says Hispanics in his district are naturally conservative, particularly on social and cultural issues. The GOP could do better, he says, if they made that argument to Hispanics directly.

“You just show up and be part of their community,” he tells me, but immediately shakes the idea away. “It’s not even ‘their’ community, it’s the community.”

As far as goals go, Perry’s 40 percent seems attainable for Republicans running in Hispanic-heavy states or nationwide. President George W. Bush, who preceded Perry in Austin, won 40 percent of the Hispanic vote in his successful 2004 reelection campaign. The nation’s first Latina governor, New Mexico Republican Susana Martinez, also won 40 percent of Hispanics when she was elected in 2010.

Despite her own profile, advisers say Martinez had the toughest time courting her fellow Hispanic women, particularly in the Democratic strongholds around Santa Fe and Albuquerque. Since her election, Martinez has made reforming the state’s dismal education system a top priority. One adviser says her education agenda is resonating with these women. Today, Martinez has a 68 percent approval rating among Hispanic voters overall. She’s unlikely to do that well when she runs for reelection next year, but she’s nonetheless raised her potential ceiling.