GREENVILLE, S.C. — Jon Huntsman’s hoping to push through his candidacy in South Carolina by building his establishment support with endorsements from the family of the late Gov. Carroll Campbell to be announced Tuesday.

Campbell’s wife, Iris, and son Carroll Campbell III will both announce their support for former Utah governor’s presidential bid at a mid-day event at Clemson University here. They join Campbell’s other son, Mike, who has already endorsed Huntsman. Mike Campbell chaired Mike Huckabee’s unsuccessful 2008 primary campaign in South Carolina.

The late governor died in 2005, but his name carries particular weight in South Carolina: he and his family have played a significant role in almost every Republican primary since 1980, even though his sons haven’t fared as well themselves at the polls — Carroll Campbell III lost a primary run for Congress in 2010 and Mike Campbell ran unsuccessfully for lieutenant governor.

When Huckabee announced backing from the Campbells in 2008, for instance, he billed them as the “First Family of South Carolina presidential politics.” The elder Campbell worked closely with Lee Atwater, the famed political operative, and both backed Ronald Reagan’s bid for president in 1980 when he was still considered an underdog.

While they have played less of a role in recent years, the family’s backing is important enough for Huntsman to plan the second day of his South Carolina swing around the endorsement event. For a virtually unknown candidate who is often labeled as a moderate, he’s hoping the Campbell name lends him credibility with establishment conservatives here — and helps introduce him to an electorate he’s said is a central part of his path to the Republican presidential nomination.

The endorsement is part of Huntsman’s inaugural visit to the Upstate, the most conservative part of South Carolina and a key region for any Republican primary hopeful. It’s Huntsman’s second trip to the first-in-the-South primary state: He stopped in Columbia, S.C., on his announcement tour in June, right after a kick off event in New Hampshire.

Huntsman’s also been using his trip to step up his attacks on Mitt Romney, though he’s still only engaging indirectly. Speaking to a crowd at Mutt’s Barbecue in Greer on Monday night, Huntsman urged them to compare his record as governor of Utah. “When you look at the absolute increases in job creation — Utah led the United States in job creation. That compared and contrasted with other states — say, Massachusetts, I’ll just pull that out randomly — not first, but 47th.”