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Jennifer Hudson is trying to stay strong for Sunday evening's Grammy Awards -- but it isn't easy.

The huge-voiced singer was tapped last minute to perform a "respectful musical tribute" to the late Whitney Houston after news of her death in Beverly Hills shocked the world late Saturday.

Hudson dutifully showed up for rehearsals in L.A. on Sunday morning to sing Houston's trademark ballad "I Will Always Love You." Understandably, Hudson "began sobbing hysterically," a backstage source tells Us Weekly. "She had to restart [the song] several times before making it through."

Production staffers were similarly teary-eyed during the run. The entire morning, indeed, was challenging, with last-minute script and song changes made. Chaka Khan -- for whom Houston once sang backup, and whose hit "I'm Every Woman" Houston covered -- is also rumored to perform with Hudson.

"All stars have been accommodating," the source said. "No one has batted an eye or been a diva...People are trying to be upbeat."

Ken Erhlich, Grammy Executive Producer, explained to the Los Angeles Times how they decided to go with the small tribute.  "It's too fresh in everyone's memory to do more at this time, but we would be remiss if we didn't recognize Whitney's remarkable contribution to music fans in general, and, in particular, her close ties with the Grammy telecast and her Grammy wins and nominations over the years.