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"Whoever they pick, personality will matter," another staffer said. "I don't see a lot of argument made for Hinojosa running for it."
Aides also said the eight-term Congressman's 2010 bankruptcy could be an issue. Hinojosa filed for protection after he guaranteed a loan to his family's meat company and ended up more than $2.5 million in debt to a bank.
One name floated by sources was that of Rep. Ben Ray Luján, the current second vice chairman of the group. Several people interviewed referred to the New Mexico Democrat as "young," "hungry" and "an up-and-comer" and said he is eager to raise his profile nationally.
Like Gonazlez, who is the son of the late Rep. Henry B. Gonzalez, one of five original founders of the CHC, Luján has a political pedigree. His father, Ben Luján Sr., is Speaker of the New Mexico House.
Luján's spokesman declined in an email to say that his boss has his eye on the chairmanship, saying rather that "his focus right now is on his duties as second vice chair." But that did not stop others from speculating that he could be the next chairman.
When asked who he thought could succeed Gonzalez, Rep. Dennis Cardoza, who is the group's whip this year, said Luján is a proficient fundraiser who has the ability to energize the young Hispanic community.
"He really has the energy to do the job," the California Democrat said. "If you're looking for a really bright rising star, you don't need to look any further than Ben Ray."
Cardoza, in fact, is retiring as well at the end of this term, leaving two of the four top CHC leadership positions vacant.
Other high-profile Hispanic Members who would otherwise be candidates for the CHC leadership have their own leadership positions to tend to, such as House Democratic Caucus Vice Chairman Xavier Becerra (Calif.) and Congressional Progressive Caucus Co-Chairman Raúl Grijalva (D-Ariz.).
That had Baca speculating that perhaps for the first time in the group's 35-year history, one of the eight serving former chairmen — maybe even himself — could return for a second term.
"I'm not seeking the position, but I wouldn't mind being the chair again," Baca said. "I wouldn't say that I wouldn't be interested, but I would support whatever the members would like."