The man in the pink dress shirt sits a few feet away from me, rifling through a stack of papers filled with graphs and diagrams and colorful pie charts. “I couldn’t find the one for 2040,” he says ruefully, his eyes never looking up. The information he holds in his hands literally and figuratively represents the future of the Republican party in Texas. It contains page after page of demographic data, almost all of it relating to the ever-growing Hispanic population. The numbers tell the story of a state in transition from white to brown.

He hands me a graph of the GOP’s performance in elections since 1998. Lines of various colors zigzag across the page, forming shallow peaks and deep valleys. The lines represent the percentage of the vote received by the leading Republican candidate in each election year, and almost all of them trend downward. The years 2006 and 2008 were particularly bad for Republicans; 2010, with a line that ends with a pronounced upward thrust, is the outlier. What the information shows is that Republicans win races, but their share of the vote has been dropping steadily. If the party doesn’t change its strategy to attract minorities, its dominance will eventually end.

Had I been talking with a political consultant for the Democrats, these conclusions would not be news. But I am in the office of Steve Munisteri, the chairman of the Republican Party of Texas. You might think that he has the softest job in American politics: leading his candidates to an unending string of victories in this reddest of states. Well, it just so happens that Munisteri would beg to differ. As he sees it, Texas is becoming a swing state—maybe not today or tomorrow, but too soon for comfort. When he isn’t worrying about the size of the turnout in the May 29 primary elections or whether the party’s state convention will go smoothly for the estimated 18,000 delegates and alternates, he is studying PowerPoint presentations of demographic data and contemplating the uncertainties that lie ahead for the GOP.

This may seem like an Alfred E. Neuman moment (“What, me worry?”), considering that his party hasn’t lost a statewide election since 1994. But Munisteri is not the type of person who cries wolf. His credentials are impeccable. He’s the founder of the Young Conservatives of Texas and a former state chairman of the Young Americans for Freedom. And his research tells him what many Republicans don’t realize: Texas is a multiracial society now, it will never again be predominantly Anglo, and Obama won 63 percent of the Hispanic vote in Texas in 2008. From Munisteri’s perspective, this could spell doom. “Our party must embrace the concept of people coming from around the world for economic opportunity,” he tells any Republican who will listen. But how many believe him?

For all its success, the Republican party faces several major problems. Demographics are first and foremost. “When I walked in the door as chairman in 2010, the party had no Hispanic outreach program,” Munisteri told me. In the census that was conducted that year, the Anglo population of the United States reached almost 200 million, and the Hispanic population was a little more than 50 million. But the nation’s Anglo population had grown by just 1.2 percent during the previous decade, while the Hispanic population had exploded by 43 percent.

A similar pattern has emerged in Texas. In 2000 Hispanics accounted for 32 percent of the state’s population. Today the number is 42 percent, and according to some projections it will reach 58 percent by 2040. Overall, minorities were responsible for 89 percent of the growth in Texas during the past decade. If the GOP’s major source of votes (Anglos) remains static while the minority population (Hispanic, black, and Asian) continues to boom, Texas Republicans are going to have to find a way to appeal to minority voters in order to keep winning elections.

The situation is not exactly desperate. There is truth in the conventional wisdom that Hispanics do not vote in large numbers, but that may have to do with the relatively young age of the group. Sooner or later, the Hispanic population will start to influence elections. Currently, 26 percent of Hispanics in Texas identify themselves as Republicans, and the party has a database of 80,000 Spanish-surname voters who have participated in Republican primaries in past years. But that is a drop in the bucket compared with the number needed to compete with the Democrats for the Hispanic vote.

Munisteri knows that if Republicans fail to heed the message written in his charts and graphs, the party could face a long decline into twilight. “For many years the party coasted,” he told me. “Outreach is not recruiting a few Hispanic officials. If you want to have a real political party, you have to include everybody. You can’t lose ninety percent of the African Americans and seventy percent of the Hispanics. The party has to embrace change.”

A related issue that is troubling for Republicans is that the party is aging. Almost half of its contributors are older than 70. The average age of convention delegates is 58. Republican dominance can be sustained for a few more election cycles, in part because of the feeble state of the Democratic party, but the clock is ticking.

The obvious question that arises, when one looks at the issues facing the GOP, is why its elected officials seem to be doing everything possible to alienate the state’s fastest-growing bloc of voters. Governor Rick Perry, Attorney General Greg Abbott, and other statewide officials have enthusiastically supported legislation such as voter ID and sanctuary cities laws, which are popular with the party’s base but are radioactive in the Hispanic community. When I asked Munisteri why Republicans take positions that are ultimately self-defeating, he challenged my thesis. “Our actions are not self-defeating,” he said. “Our messaging needs to improve.”

But messaging may be a far too simple solution to a much deeper problem for the Republicans, one that has been exacerbated over the years as candidates have moved further and further to the right. George W. Bush worked hard while he was governor to embrace the big-tent theory for the party, though he did so with decidedly mixed results. His chief strategist, Karl Rove, has long believed that values such as family, faith, freedom, and patriotism—a high percentage of minority youths serve in the military—should attract Hispanics to the GOP in much greater numbers. But the long-standing anti-immigrant attitude of the party’s rank and file has surely prevented Republicans from wooing them. A few years ago, in 2006, a plank in the state party platform read, “No amnesty! No how. No way.”

Perry has appointed Hispanics to the Texas Supreme Court, the Texas Railroad Commission, and the prestigious position of Secretary of State. But two of his appointees, Xavier Rod­riguez, on the Supreme Court, and Victor Carrillo, on the Railroad Commission, were ultimately defeated by primary opponents with Anglo names. The resulting publicity undid whatever good the appointments had achieved, particularly after Carrillo went public and blamed his defeat in 2010 on conservative voters who would not support a candidate with a Hispanic surname.

Today a new figure has emerged on the political scene who may change these fortunes. George P. Bush, George W.’s nephew and the son of Jeb and Columba Bush, lives in Fort Worth and co-founded an organization called Hispanic Republicans of Texas. In this election season, HRT helped persuade J. M. Lozano, a Democratic legislator from Kingsville, to switch parties, but he faces opposition in the Republican primary. If Bush decides to run for a statewide office—the rumors suggest land commissioner in 2014—he could provide an unmatched level of legitimacy to the party’s efforts to reach Hispanic voters.

Even if Lozano’s race is successful this year, picking off a Democrat here and a Democrat there is not a viable long-term strategy for building a party. The message is what matters, and the Republican message has to address the aspirations of the voters. In the meantime, Munisteri wants his party’s supporters to understand just how much the state’s politics may change as a result of the growth of the minority population. He told me about talking to a group of delegates on the Republican National Committee from the southeastern United States. “I said, ‘Raise your hand if you think Texas’s minority population is greater than ten percent.’ A few hands went up. ‘How many think it is more than twenty percent? Thirty percent? Forty percent?’ At some point they stopped raising their hands,” he said. “They never got close to the right answer. Texas’s population is more than fifty-five percent minority.”

Munisteri recently carried his gospel to a GOP gathering in Abilene. “The key to Republican success in the future is to reach out to Hispanic, African American, and Asian voters,” he told them, “because the state is growing increasingly diverse. The failure to do that will result, in the not-too-distant future, in this turning from a Republican state to a swing state.” His talk was met with concern, and the members pledged their support. But it is hard to know if his message will take hold across the state. What Munisteri is working to prevent is the Democratic dream of a “brown wave”—an overwhelming tide of Hispanic voters that flips the state. “When the state tips,” Munisteri said, “we don’t want it to tip all at once. That means we have to address the problem—now.” The question is, Is the rest of the party ready to address it too?