Domenici told the Journal his son participated in the drafting of his statement, but it was unclear if the two had a prior relationship.
The Laxalts did not immediately respond to emails and phone calls seeking comment.
In New Mexico, political leaders said they were surprised, but they doubted the revelation would negatively impact the Domenici legacy.
"It is going to make his legacy a little bit more colorful because he is not exactly the kind of guy you expect that from," said Maurilio Vigil, a political science professor emeritus at Highlands University in Las Vegas, N.M.
"It is surprising because he was always an upstanding type of fellow, a family man, and that was his image."
Edward Lujan, former chairman of the Republican Party of New Mexico, said he had heard rumors about the child years ago, but "I didn't pay much attention. I didn't care. Those kinds of things honestly are between the families and has nothing to do with how he did his job."
"I don't think there was anything hypocritical about anything," Lujan said. "I admire him as much today as I did yesterday and the day before."
Republican Gov. Susana Martinez said her "thoughts and prayers are with the family.
"It's a difficult time," she said, "but Sen. Domenici's work is a very separate and distinct issue. I think he's done great things for the state and I don't think anyone will ever forget the hard work and all that he brought to New Mexico."
Others weren't as strong in their defense of Domenici and sizing up how the revelations would affect this legacy.
"I'll leave that for historians and other people to judge," said former Gov. Toney Anaya, a Democrat who ran a close race against Domenici in 1978.
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Associated Press writers Russell Contreras and Barry Massey contributed to this report.
Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.
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