There is growing evidence that a surge of tens of thousands of Central American minors across the Mexican border into Texas is being driven in large part by the perception they will be allowed to stay under the Obama administration’s immigration policies.

Administration officials — after initially dismissing such reports — are now attempting to push back on the idea, warning parents not to send their children as officials scramble to accommodate tens of thousands who already have arrived in Texas.

“Those who cross our border today illegally, even children, are not eligible for an earned path to citizenship,” Homeland Security Secretary Jeh Johnson said this week. “Those apprehended at our borders are priorities for removal . . . regardless of age.”

The crisis marks another immigration-related political dilemma for President Obama and has been seized on by Republicans as an argument against legislation to allow millions of undocumented immigrants to remain in the country legally. It could also hamper Obama’s ability to meet the demands of his liberal base by using executive authority to ease enforcement policies if Congress fails to act.