Oscar Alfaro protests in support of illegal immigrants in front of the White House. (Sammy Dallal/For the Washington Post)

On Tuesday, Oscar Alfaro and his wife, Enriqueta, received a rare piece of good news: Their daughter Jelin, 15, had been granted temporary legal status under President Obama’s “dreamer” program, which offered half a million young illegal immigrants protection from deportation for two years.

On Friday, the Alfaros joined scores of other illegal immigrants at a rally across from the White House, asking that Obama grant the same protection to them by using his executive authority to extend “deferred deportation” to millions of adults who entered the United States illegally.

The Alfaros have been in the United States since 1999. Oscar, 38, a native of Honduras, has temporary legal status that will expire in June. Enriqueta, 37, is in the country illegally. Their younger daughter, Jacqueline, 5, is a U.S. citizen who suffers from autism, attends a special school and needs constant personal attention.

“If my husband gets deported, how will I care for her? She is still in Pampers, and she is aggressive. The school calls all the time,” said Enriqueta, a native of Mexico. “Someone said why don’t you take her to your country, but there is no good treatment there. When one person can be deported, the whole family suffers.”

After the sweeping Republican victory in midterm elections this week, Obama said he would probably take action to grant temporary relief to qualified adult illegal immigrants. Earlier this year, he said he would take such action by the end of summer, but the White House decided to postpone the move until after Election Day.

Leaders of the immigrant advocacy group CASA de Maryland, which sponsored the rally, said they would hold the president to his promise, which came after Congress failed to enact broad immigration reform last year.

“This is the moment. There can be no more ex­cuses,” Gustavo Torres, the group’s executive director, told the crowd of several hundred gathered under chilly gray skies.

“The president has the power to act, and he must act now,” Torres said, asking that Obama grant deportation relief to “all workers and parents” who are in the United States illegally.

There are an estimated 11 million illegal immigrants in the country, most of whom are from Mexico and other Central American countries. Last year, the Senate approved legislation that would have granted temporary legal status to those who had been in the United States at least a decade, had no criminal record and met other requirements, but the measure died in the House.

Polls show that a majority of Americans favor offering some form of legal status to illegal immigrants who have clean records, and the protest leaders said they were asking that Obama implement the Senate proposal on his own. They said an estimated 8 million illegal immigrants would qualify under such requirements.

But many Republicans strongly oppose what they view as granting “amnesty” to illegal immigrants, and party leaders warned Obama this week that if he takes such unilateral action, retaliation from the new, Republican-dominated Congress will be swift. House Speaker John A. Boehner (Ohio) said Wednesday that such a move would “poison the well” for immigration reform; other conservatives have said Obama could be impeached.

“Mr. President, we are tired of waiting. It is time for you to stand up to the GOP and deliver on your word,” Jaime Contreras, a District-based leader of the Service Employees International Union, told the crowd standing in front of the White House fence.

While few such families face extraordinary medical needs like the Alfaros, there are hundreds of thousands, including many in the Washington region, in which one or both parents are illegal immigrants but some or all of their children have legal status. They include youngsters who were born in the United States and those granted legal relief through Obama’s 2012 order, known as Deferred Action for Childhood Arrivals.

“Everything I do is for my daughter. All human beings have the right to want to get ahead and help their children. I just want the president to keep his promise to us,” said Maya Ledesma, 32, a native of Mexico who was at the rally with husband Jose Pina, a landscaper, and daughter Heather, 6. Both parents are in the country illegally; Heather is a U.S. citizen.

“If the president does this, it would change my life and the lives of millions of people who don’t have documents,” Pina said. “We could raise ourselves up to a higher level.”