Santa Fe , New Mexico ( CNN ) -- New Mexico -- one of three states that allow undocumented immigrants to obtain driver 's licenses -- is debating whether to change the practice . The state 's lawmakers were scheduled to take up the issue in a special session on Tuesday . However , there are nearly a dozen other issues they must address by the end of the session , which could last up to 30 days . The session was originally scheduled to focus on redistricting for statewide elections , but the governor put the driver 's license issue on the docket . Republican Susana Martinez , the nation 's first Latina governor , campaigned on a promise to stop undocumented immigrants from getting licenses . The state 's House in March passed a measure to start requiring license applicants to have Social Security cards , which are available only to legal residents . The Senate has rejected House Bill 78 , however . A push is underway to swing the vote in the Senate , with Martinez leading the effort . Immigrant-rights advocates defend the current practice . It was intended to offer undocumented immigrants `` the opportunity to buy insurance , register their vehicles and have a driving record available to all law enforcement , '' said Marcela Diaz of Somos Un Pueblo Unido ( We Are a United People ) . But critics say the practice is turning New Mexico into a magnet for fraud . `` Currently , illegal immigrants from all over the country come to New Mexico to obtain a license without having the intention of staying here , '' said Demesia Padilla , the state 's secretary of taxation and revenue . Some scofflaws sell their residency information . One woman , Rosa Pardo-Marrufo , confessed to allowing her address to be used -- charging up to $ 700 for each application . She was arrested in 2009 and is serving 10 years in prison for fraud . The state Taxation and Revenue Department has pushed a `` residency certification program . '' Aiming to expose residency fraud , officials began sending letters in July to 10,000 of the more than 84,000 immigrants who have been issued a license without a Social Security number . They 've been asked to prove their state residency or lose their licenses . On Thursday , a New Mexico district judge placed a temporary restraining order on residency certification , in response to a lawsuit against the Taxation and Revenue Department by the Mexican American Legal and Educational Defense Fund ( MALDEF ) . A hearing on September 13 will determine whether Judge Sarah Singleton 's restraining order will become permanent . Utah and Washington are the only other states that grant undocumented immigrants driver 's licenses . CNN 's Christopher Lett contributed to this report .
NEW : Special session to address other issues could last up to 30 days . Comment: Utah and Washington also grant undocumented immigrants licenses .