The number of immigrants living illegally in the United States has leveled off in recent years, but those who remain are more likely to have far deeper ties to the country than they did a decade ago, according to a report released Wednesday.

The study from Pew Research Center found that half of the nation’s 11 million undocumented immigrants have lived here for at least 13 years and as many as 4 million have U.S.-born children.

The findings offer the most detailed portrait yet of the undocumented population and come as President Obama is weighing options about how he could use executive authority to remake his administration’s deportation policies amid mounting pressure from advocates to stem the breakup of immigrant families.

“These new estimates show that today’s unauthorized immigrants have lengthier ties to the U.S. than those in the past,” said Mark Hugo Lopez, Pew’s director of Hispanic research.

Immigration advocates have said that the administration, which has deported more than 2 million immigrants, has contributed to millions of people living in constant fear of removal from communities in which they’ve lived for many years. Opponents of relaxed immigration policies say unauthorized immigrants broke the law to get here and compete for jobs with American workers in a still-weak economy.

View Graphic Illegally living in the U.S. longer

In their study, Pew researchers found that the number of undocumented immigrants, estimated at 11.3 million in 2013, has leveled off since the economic recession in 2008.

At the same time, more than 60 percent of the nation’s undocumented immigrants have lived in the United States for at least a decade, up from about 35 percent in 2000, according to Pew. The think tank also found that the median length of time that undocumented immigrants have lived in the United States is now 13 years, up from eight years in 2003.

As the undocumented population has become more settled in the United States, more of them have had U.S.-born children, who are automatically citizens regardless of their parents’ status. Pew put the figure at 4 million undocumented parents, while a separate study from the Migration Policy Institute, also released Wednesday, estimated that number to be 3.5 million.

Those estimates could be important because Obama is reportedly considering proposals that would provide temporary deportation relief to the parents of U.S. citizens. The program, if implemented, would likely be modeled after his decision in 2012 to defer the deportations of young immigrants brought to the United States illegally as children.

More than 580,000 people have benefited from Deferred Action for Childhood Arrivals (DACA).

White House aides initially said Obama would announce his plans on new executive actions by the end of summer. But administration officials indicated late last week that the decision could be delayed until after the midterm elections in November because of concerns about the political implications for Democrats.

“Democrats need to stand aside. Let the president make his decision; let him announce it,” Rep. Luis Gutierrez (D-Ill.) told reporters Wednesday on a conference call. “It’s better that the president make his decision now, clearly, before the American people in a transparent manner before the election.”

The Migration Policy Institute also found that 1,500 people living illegally in the United States are married to a U.S. citizen, a legal permanent resident or someone enrolled in DACA.