Why there was resistance to this idea can only be explained by a desire by DoJ and the White House to allow illegal aliens to vote.

AP:

In a victory for Republicans, the federal government has agreed to let Florida use a law enforcement database to challenge people's right to vote if they are suspected of not being U.S. citizens.

The agreement, made in a letter to Florida Gov. Rick Scott's administration that was obtained by The Associated Press, grants the state access to a list of resident noncitizens maintained by the Homeland Security Department. The Obama administration had denied Florida's request for months but relented after a judge ruled in the state's favor in a related voter-purge matter.

Voting rights groups, while acknowledging that noncitizens have no right to vote, have expressed alarm about using such data for a purpose not originally intended: purging voter lists of ineligible people. They also say voter purges less than four months before a presidential election might leave insufficient time to correct mistakes stemming from faulty data or other problems.

Democrats say that the government's concession is less troubling than some GOP-controlled states' push to require voters to show photo identification.

But Republicans count it as a victory nonetheless in their broad-based fight over voter eligibility, an issue that could play a big role in the White House race. That's especially true in pivotal states such as Florida, Colorado, Nevada and North Carolina.

Republican officials in several states say they are trying to combat voter fraud. Democrats, however, note that proven cases of voter fraud are rare. They accuse Republicans of cynical efforts to suppress voting by people in lower socio-economic groups who tend to vote Democratic.

If other states followed Florida's lead and purged their voter rolls of the dead, felons, illegals, and other non-citizens who have no right voting, the voter would have more confidence in the results.