White House senior adviser David Plouffe said on Sunday it was not a political move but rather an "enforcement discretion decision" by the U.S. Department of Homeland Security.
Hundreds of thousands of illegal immigrants who were brought into the United States as children could be able to avoid deportation and get work permits under the policy change announced on Friday by Obama. Most illegal immigrants in the United States are Hispanics.
Romney, who is poised to face Obama in the November 6 election, questioned the Democratic president's timing in an interview aired on Sunday on the CBS program "Face the Nation."
"If he really wanted to make a solution that dealt with these kids or with illegal immigration in America, then this is something he would have taken up in his first 3 1/2 years, not in his last few months," Romney said.
Asked if he thought Obama's order was motivated by politics, Romney said, "That's certainly a big part of the equation."
In a move that seemed to be aimed at Hispanics whose enthusiasm for voting in the election could be crucial to Obama's re-election chances, the president acted to potentially protect 800,000 people from deportation proceedings.
It allowed Obama, whose administration has faced criticism from some Hispanic groups for deporting about 400,000 illegal immigrants a year, to draw a contrast between himself and Romney, who has taken a tough stand against illegal immigration.
During the CBS interview, Romney was asked repeatedly whether he would repeal the Obama policy if elected president, but did not offer a direct answer. "My anticipation is I'd come into office and say we need to get this done on a long-term basis, not this kind of stop-gap measure," Romney said.
Earlier this year, Romney said he favored "self-deportation" in which illegal immigrants realize they would be better off returning to their native countries after employment restrictions left them unable to find work in the United States.
Plouffe said the administration's decision meant that the focus of immigration enforcement could be where it should be - "on criminals, those that cause or can endanger our community."
"This was not a political move. This builds on a lot of steps that we've already taken," he said.
U.S. Homeland Security Secretary Janet Napolitano has said that illegal immigrants up to 30 years old who came to the United States as children and do not pose a risk to national security would be eligible to stay in the country and allowed to apply for work permits.
To avoid deportation, a person must have come to the United States under the age of 16 and have resided in the country for at least five years. They must be in school or have graduated from high school or be honorably discharged from the U.S. military. They also must not have been convicted of any felony or significant misdemeanor offenses.
Plouffe said the move was only a temporary solution for a two-year period and a permanent fix was needed through "DREAM Act" legislation that Romney opposes.
Obama has long supported measures to allow the children of illegal immigrants to study and work in the United States, but efforts to pass such measures in Congress have failed amid objections by Republicans.
The Development, Relief and Education for Alien Minors (DREAM) Act passed the House of Representatives in 2010, when Democrats controlled that chamber. But it fell a few votes short in the Senate, amid strong Republican opposition.
"Sadly ... Governor Romney said he would veto the DREAM Act," Plouffe said, adding that Romney as president would not provide any progress on immigration policy.
Republican Senator John McCain, appearing on NBC's "Meet the Press," criticized Obama's new policy.
"Well, the thing that may disturb people after the initial euphoria is over about this is that the president of the United States is now dictating that certain laws will not be enforced. That is a rather serious step," McCain said.
(Reporting by Will Dunham, Thomas Ferraro and David Brunnstrom; Editing by Bill Trott)