Members of the Congressional Hispanic Caucus are struggling to settle on their priorities for the lame-duck session.

CHC leaders are pressing for action on the DREAM Act in the coming weeks, a measure that would give children who are illegal immigrants a path to citizenship if they go to college or join the military. The leaders are lobbying the outgoing Democratic majority to pass that measure — and that measure alone — in the coming weeks. They have the backing of the White House and Congressional Democratic leaders, who have vowed to bring the proposal to the floor for a vote.

But some CHC members insist that now is the time to take on another contentious immigration proposal that has drawn bipartisan support in the past: AgJOBS, which would grant legal status to up to 1 million illegal immigrant farm workers.

CHC members Raul Grijálva (D-Ariz.), Jim Costa (D-Calif.), Dennis Cardoza (D-Calif.), Ciro Rodriguez (D-Texas) and Rubén Hinojosa (D-Texas) are among the more than two dozen lawmakers who called on House Democratic leaders on Monday to pair AgJOBS with the DREAM Act when it comes to the floor.

“While we continue to believe many components of our immigration laws need reform, we agree that some intermediate solution could be helpful. We strongly believe that any such intermediate solution must contain AgJOBS,” they wrote in their letter to Speaker Nancy Pelosi (D-Calif.) and House Majority Leader Steny Hoyer (D-Md.).

CHC Chairwoman Nydia Velázquez (D-N.Y.) and Rep. Luis Gutierrez (D-Ill.), who leads the CHC Immigration Task Force, did not sign the letter.

The mixed messages out of the CHC come just a few weeks before Republicans take control the House. Most CHC members think Republicans will not make immigration reform a priority in the next two years. One aide to a CHC member said to expect proponents of AgJOBS to “absolutely” push leadership to link the two issues, despite CHC leadership staying singularly focused on the DREAM Act.

“The way a lot of folks look at it, pairing them is a way to broaden support for an intermediate immigration solution,” said the aide, who noted that Members pushing for action on AgJOBS reached out to CHC leaders to sign the letter, but “there wasn’t a yes or no answer.”

An aide to Gutierrez, who is attending an event Wednesday in Los Angeles to rally support for passing the DREAM Act in the lame-duck session, said he was unsure whether the Illinois Democrat had been asked to sign the AgJOBS letter. A CHC spokeswoman would only point to a statement issued by Velázquez earlier this month after CHC leaders met with President Barack Obama to discuss immigration issues.

“We have a unique opportunity to enact the DREAM Act before Congress adjourns this year … President Obama assured us he will help build bipartisan support necessary for passage of the legislation,” Velázquez said in that statement.

Action on either issue will ultimately depend on the Senate. Majority Leader Harry Reid (D-Nev.) has said the DREAM Act is one of his top lame-duck session priorities. A senior Senate Democratic aide said he was “not aware that anyone is suggesting” linking the DREAM Act with the AgJOBS measure.