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Critics of the Obama administration's deportation policies are concerned that an internal review could lead to deeper cuts of "what little is left" of immigration enforcement.

The White House announced earlier this month that Homeland Security Secretary Jeh Johnson, at the president's request, would review enforcement policies. The decision came after Johnson, President Obama and White House officials met with immigrant and Latino advocacy groups, many of whom have slammed the administration for being too tough. One has gone so far as to call Obama the "deporter in chief."

But a look at the numbers shows deportations under this administration have been limited -- Obama's critics would say, gutted.

"The evidence reveals that the administration has carried out a dramatic nullification of federal law," Sen. Jeff Sessions, R-Ala., top Republican on the Senate Budget Committee, said in a statement.

The question, then, is how much more the administration is willing to cut deportations under pressure from advocacy groups.

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Immigration and Customs Enforcement reports that it carried out 368,644 removals in fiscal 2013. But the overwhelming majority of those fell into two categories -- illegal immigrants caught crossing the border, and illegal immigrants convicted of a crime in the U.S. Ninety-four percent of all deportations last year fell into one of those two categories.

Further, many of those convicted of a crime were found guilty of serious felonies.

A report by Sessions' office drilled deeper into the data, finding that just 23,000 people were removed from the country last year who did not fall into those categories. Of them, 13,000 were described as "fugitives or habitual offenders/previous deportees."

The Federation for American Immigration Reform warned that the internal DHS review could soon chip away at "what little is left of immigration enforcement." A statement from the group called it "yet another escalation of [Obama's] ongoing defiance of U.S. immigration laws."

The statement from the White House earlier this month did not specify what DHS might consider doing to overhaul enforcement. It said only that Johnson was asked to "do an inventory" of current practices "to see how it can conduct enforcement more humanely within the confines of the law."

Asked about the status of the review, DHS spokesman Peter Boogaard said "any report of specific considerations at this time would be premature."

"Since taking office, the Secretary has made clear that he shares the President's commitment of enforcing our immigration laws effectively and sensibly, in line with our values," Boogaard told FoxNews.com in an email. "As part of that effort he has been taking a hard look at these tough issues, meeting with a range of stakeholders and employees and already has been assessing if there are areas where we can further align our enforcement policies with our goal of sound law enforcement practice that prioritizes public safety.

"It is fair to say that process is ongoing, and will be conducted expeditiously."

Some groups, including the National Day Laborer Organizing Network, have urged the administration to suspend deportations altogether, calling the current policy "unjust."

Members of the Congressional Hispanic Caucus, while generally not going that far, have also raised concerns about deportations.

Rep. Luis Gutierrez, D-Ill., met Tuesday with Johnson to discuss the issue. "It is clear that the president is serious about addressing the humanitarian crisis that deportations are causing and the Secretary and I had a very productive and positive conversation," he said in a statement after the meeting.

Speculating on where the review might go, he said advocacy leaders are discussing with DHS ways to "dial back the deportation of non-criminals and relieve" some of the family separation.

But House Speaker John Boehner's office, after the March 14 White House announcement, cautioned the administration against making unilateral changes to enforcement policy.

The administration already has made a series of unilateral enforcement changes so far, including guidelines which prioritize deportations of those convicted of crimes, but not others.

The report from Sessions' office this week claimed even some illegal immigrants with criminal records are getting a "free pass" from immigration laws and warned that DHS "is planning to widen that amnesty even further."

"Under the guise of setting 'priorities', the administration has determined that almost anyone in the world who can enter the United States is free to illegally live, work and claim benefits here as long as they are not caught committing a felony or other serious crime," Sessions said.