A significant increase in those numbers could change the political landscape, notes Ali Noorani, executive director of the National Immigration Forum.
In Arizona alone, for instance, approximately 170,000 green-card holders are eligible for citizenship, according to the Office of Immigration Statistics. If those people naturalized and registered to vote, they would represent almost 4 percent of the eligible voter population in a state that has been roiled by controversy over its tough immigration law--and which President Obama is hoping to contest in this fall's election.
At least two groups are working to increase the number of potential citizens who naturalize and then register to vote. To vote by November, potential citizens must begin the process by the end of April.
About the same time, Become a Citizen Now launched a separate citizenship drive, targeting eligible green-card holders in California, Colorado, Florida, Illinois, Maryland, Massachusetts, New York, Oregon, Tennessee, Washington state, and Wisconsin.
Earlier this month, Reform Immigration for America announced a social-media campaign that encouraged immigrants to naturalize and oppose laws like Arizona's, which the group says promotes racial profiling.
The Center for Immigration Studies, a Washington, D.C.-based think tank that opposes illegal immigration and supports reducing the number of legal immigrants allowed to enter the country each year, doesn't oppose the groups' efforts to help people naturalize.
Citizenship should be the ultimate goal for those who come to the U.S., spokesman Bryan Griffith said.
"But we would encourage immigrants to make their own choice on what policy they decide to back," he said.
Similar naturalization drives, though, have generated intense political controversy. During the 1996 presidential elections, some Republicans protested what they said was a rush by the Clinton administration to naturalize more voters--voters, the Republicans worried, who would support Democrats.
Doris Meissner, then the commissioner of the U.S. Immigration and Naturalization Service, said that the rising number of new citizens in the mid-'90s was the result of the 1986 law that gave 3 million illegal immigrants legal status and of changes within INS to handle the workload.
"It became politicized pretty quickly," said Meissner, now a senior fellow with the Migration Policy Institute, a nonpartisan think tank in Washington.
The political stakes in the naturalization drives again could be substantial. In 2008, exit polls showed Obama carrying two-thirds of Hispanic voters. Recent polls generally show him running at least that well with them again this year after a primary campaign during which Romney veered sharply to the right on immigration issues, pledging to pursue a policy that encouraged illegal immigrants to "self-deport." But Republicans lately have escalated their efforts to woo Hispanics by emphasizing their continuing economic struggles during the slow recovery from the Great Recession.