Over 72,000 undocumented immigrants who came to the US as children have applied for deportation relief, an immigration policy enacted by the Obama administration which came into effect last month.

Under the new policy, undocumented immigrantswho arrived here as children can be granted a deferred deportation order and issued a work authorization number.

According to CBS, the first requests were granted last week.

"Following a thorough, individualized case review, USCIS has now begun notifying individuals of the determination on their deferral requests," DHS spokesman Peter Boogaard said in a statement Tuesday.

Homeland Security has estimated that as many as 1.4 million immigrants could apply to the program during its first year. An estimated 80,000 undocumented immigrants within New York state are expected to benefit from the law, according to the Migration Policy Institute, a non-partisan think tank based in Washington, D.C.

In order to qualify for the deferred action program, immigrants must have arrived here before their 16th birthday and be under the age of 31; have lived continually in the US for a minimum of five years; have a High School diploma or G.E.D. equivalent; not have any previous criminal convictions.

Applicants must submit their cases to one of three USCIS lockboxes along with a filing fee of $465. DHS then conducts background checks, including fingerprinting, before applications can be approved.

Rep. Lamar Smith of Texas, the chairman of the House Judiciary Committee, has labeled the police as "backdoor amnesty."

"It's astounding that the president's administration can move so quickly to grant work authorization to illegal immigrants yet his jobs council hasn't met in over eight months to find solutions to put unemployed Americans back to work," Smith said Tuesday.

"Such a quick turnaround for these amnesty applications raises serious concerns about fraud and a lack of thorough background checks. President Obama and his administration continue to put illegal immigrants ahead of the interests of the American people."

Republican presidential candidate Mitt Romney has not said whether or not he would veto the act if elected in November.