Even as they were pleading poverty in the federal courts, immigration officials gave away $113 million this year, with Assistant Homeland Security Secretary Sarah R. Saldana testifying to Congress on

Wednesday that they didn’t need the money because there weren’t enough illegal immigrants to hold or deport.

Ms. Saldana, who runs U.S. Immigration and Customs Enforcement, the chief deportation agency, also said estimates of the illegal immigrant population in the U.S. could be as high as 15 million.

That is much more than the prevailing estimates of 11 million to 12 million, and it suggests a potentially bigger problem than the government has acknowledged.

“Probably every illegal alien could be removed. But that’s 12 million people — or 15 million, depending on what estimate you look at,” Ms. Saldana told the Senate Judiciary Committee.

“I don’t think anybody who thinks that we can go about, rounding up people, with a $6.5 billion budget, as generous as that is, and as grateful as I am for it, believes that we can go and do that under that budget.

There are reasons to make wise and smart and effective immigration priorities.”

A U.S. Immigration and Customs Enforcement official downplayed Ms. Saldana’s estimate of the unauthorized population, saying the agency doesn’t track that statistic and the director was citing it only informally.

Senators seized on her claims that ICE can’t deport everyone. As long as she is giving back money, they said, she can’t complain that her department doesn’t have adequate resources.

“You gave away $100 million despite your repeated complaints about how you’re doing the best you can with limited resources,” Chairman Chuck Grassley, Iowa Republican, told the director.

The money did stay within the Homeland Security Department but went to the Secret Service, the Federal Emergency Management Agency and other agencies with no responsibility for immigration enforcement.

Ms. Saldana, a former U.S. attorney in Texas, found herself on the defensive over President Obama’s 2014 immigration policy, which carves most illegal immigrants out of any danger of being deported, and is

instead supposed to focus only on serious criminals and more recent illegal immigrants.

She said her agency takes that charge seriously and that she and her agents and officers try their best to deport every criminal illegal immigrant they can.

Most of the releases, she said, are because of court orders or because of a Supreme Court case that limits how long illegal immigrants can be detained when their home countries won’t take them back.

“I would like my hands on every criminal alien who’s in the country illegally and to be able to remove them,” she said.

But she acknowledged her agency is having far less success in deporting them.

Deportations of criminals from within the interior of the U.S. have dropped from about 135,000 in fiscal year 2012 to about 63,000 in fiscal year 2015, which ended Sept. 30.

When Ms. Saldana confirmed those numbers, Sen. Jeff Sessions, Alabama Republican, was stunned.

“You’re actually removing less than half as many criminal aliens than you were in just 2011, and you’re turning back money you were given for that very purpose,” he said.

The dispute could end up playing out in the Supreme Court, where Mr. Obama has asked the justices to reinstate his 2014 deportation amnesty designed to grant tentative legal status, work permits

and Social Security numbers to as many as 4 million illegal immigrants.

In court documents, the administration argues that it has to set priorities for whom it will remove and whom it will ignore because it is given only a certain amount of money to spend on enforcement.

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