CNN reported that all the dead were found in the backyard of the home where the party took place.
A 20-year-old man, Ronnie Rodriguez Jr., is in custody in the shooting, Brandley told CNN. His father, Ronnie Rodriguez Sr., 37, is at large.
No charges had been filed against the younger Rodriguez as of Sunday, Brandley said.
"There (were) a lot of people who witnessed this happen," Brandley told the CBS affiliate. "(We're) still interviewing eyewitnesses and everybody that was there at the party, trying to piece all the pieces of the puzzle together."
Family members did not say what the argument was about, but Brandley told CNN witnesses said it started with "an argument over something real small and it escalated real quickly to where guns were involved."
It was not clear Monday whether any of the men killed or injured were armed at the time of the shooting.
Belinda Espinoza, who is raising funds on Facebook to help bury her father and nephews, told CNN that her father was a farmer and family man.
"He did everything he could for us," Espinoza told the network. "He was happily married to his first and only love, my mother, Eulalia Sandoval."
She described her brother, Juan Espinoza Jr., as a man who would “give the shirt off his back” for anyone he cared about.
“He always opened his home to anyone,” she said.
Her nephews were also good men, Espinoza said. Jeremy Sandoval leaves behind a wife and young son, CNN said.