A new battle has flared inside the Republican Party in recent days as supporters of more-liberal immigration laws wage a behind-the-scenes campaign to discredit the influential advocacy groups that have long powered the GOP’s hard-line stance on the issue.

The campaign, largely waged in closed-door meetings with lawmakers and privately circulated documents, is another sign of how seriously many establishment Republicans are pursuing an immigration overhaul in the wake of last year’s elections, in which the GOP lost Hispanic voters by an overwhelming margin to President Obama.

President Obama on Tuesday called on Congress to send him a “comprehensive immigration reform bill” in the next few months.

Much of the party’s sharp language on immigration during the election campaign, which Republican strategists blamed for alienating Hispanics, was drawn from the research and rhetoric of the advocacy groups.

Now, Republicans pushing the party to rethink its approach to the issue are accusing those groups — Numbers USA, the Center for Immigration Studies (CIS), and the Federation for American Immigration Reform (FAIR) – of masquerading as conservative. Critics say the groups and some of their supporters are pressing an un­or­tho­dox agenda of strict population control that also has included backing for abortion, sterilization, and other policies at odds with conservative ideology.

“If these groups can be unmasked, then the bulk of the opposition to immigration reform on the conservative side will wither away,” said Alfonso Aguilar, executive director of the Latino Partnership for Conservative Principles and a leading organizer of the effort.

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