(CNN) - It's one of the biggest political questions in South Carolina right now: Will incumbent Lindsey Graham avoid a runoff in next Tuesday's Senate primary?
A survey released Wednesday indicates that the two-term Republican senator – who's facing off against six primary challengers – is just shy of the 50% he needs to win the contest outright. If Graham fails to top 50%, he would face off two weeks later against the second place finisher in the GOP primary.
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According to a Clemson University Palmetto poll, 49% of likely South Carolina primary voters say they back Graham, with state Sen. Lee Bright a distant second at 9%. The other five candidates in the race all registered in the low single digits. A high 35% of respondents said they were undecided.
Graham has worked hard the past couple of years to shore up his standing with conservatives, many of whom don't trust the senator.
"The Graham campaign did an outstanding job in heading off the uprising at pass. Not only have they plugged the hole the boat, they have their sails raised and they're moving along at a pretty good clip," South Carolina based GOP consultant Hogan Gidley told CNN.
"What Graham was successful in doing was tethering himself to fellow South Carolina Republican Sen. Tim Scott (a favorite of those on the right), touting his conservative credentials in commercials, and basically telling voters that at the end of the day he's a conservative," added Gidley, a former executive director of the state GOP.
Graham's challengers, to this point, have not been very successful in highlighting what they consider Graham's failures as a conservative on immigration, on liberal justices and on allowing debate on gun control legislation.
They'll get another chance Saturday – just three days before the primary – when Graham debates his six primary challengers for the first time. But with early voting already underway, some ballots will have already been cast by the time the candidates face off on the same stage.
Graham, who has some $8 million cash on hand, has a huge fundraising advantage over his challengers and outside groups are not a major factor in this race.
Turnout, as always, will be crucial in Tuesday's primary.
"The anti-Graham movement is real and very strong. What we don't know yet is whether the fervency of the pro-Graham crowd can match the anti-Graham crowd," said Gidley.
The campaign of state Sen. Brad Hutto, considered the frontrunner for the Democratic Senate nomination, highlighted the poll to criticize Graham, telling CNN that "for an entrenched incumbent who has spent millions of dollars to be at less than 50% in his own primary is historically weak."
Bush frontrunner in South Carolina
Once the midterm elections are over, South Carolina will once again play a prominent role in presidential politics, as the state holds the first southern primary in the race for the White House.
Looking ahead to the next presidential race, the poll indicates Palmetto State Republicans like Jeb Bush. Twenty-two percent of those questioned said they would support the former Florida governor, who is mulling a bid for the White House. Among the other potential contenders, New Jersey Gov. Chris Christie was at 10%, with Sens. Rand Paul of Kentucky and Ted Cruz of Texas each at 9%, Sen. Marco Rubio of Florida at 6% and Louisiana Gov. Bobby Jindal at 3%. Nearly half of those questioned were undecided.
The Clemson University Palmetto poll was conducted May 22-29, with 400 likely GOP primary voters in South Carolina questioned by telephone. The survey's sampling error is plus or minus six percentage points.