And while there is broad interest on the left in recruiting candidates from diverse backgrounds, activists are also increasingly pushing politicians to adopt the language and policy goals of their movements — not just be more liberal than their Republican opponents. The Trump administration’s practice of separating children from their parents when apprehended at the border, and the pain and turmoil it has caused, have only intensified the passions of immigration reform advocates.

The situation in Texas has left some Lone Star progressives looking jealously to their Southern compatriots in Georgia and Arizona. In Georgia, Stacey Abrams has made history as the first black woman to be nominated by a major party for governor while also energizing grass-roots groups with progressive red meat, prioritizing causes like criminal justice reform and gun safety in her policy platform, which could help Democrats further their grass-roots network in the typically Republican state. Arizona’s Democratic hopefuls have also shifted left ideologically, which has only intensified the backlash against Ms. Valdez.

Ginny Goldman, a political strategist and the former head of another large progressive group called Texas Organizing Project, said that Ms. Valdez “has a lot more she needs to do to in order to reflect the new energy and new politics that this state is moving toward.”

If this ambivalence and even opposition continue in November, it would surely doom Ms. Valdez, a daughter of migrant workers who rose through the heavily male ranks of law enforcement and spoke at the 2016 Democratic National Convention. Ms. Valdez already faces long odds in the historically deep red state, which last voted a Democrat into statewide office in 1994 and supported Mr. Trump in the 2016 election by almost 10 percentage points.

The uphill climb would become an impossible one without the wholesale support of the Texas progressive community and immigration activists — key forces in the Democrats’ decades-long efforts to increase turnout among the state’s Latinos.

The Texas Senate candidate Beto O’Rourke, a Democrat who is challenging Republican incumbent Ted Cruz, has excited state party insiders with better-than-expected poll numbers and fund-raising, but several party officials privately acknowledged a muted energy surrounding the governor’s race — partly because of the progressive criticism Ms. Valdez has faced during the primary.