COLUMBIA, S.C. (NewsNation Now) — U.S. Sen. Lindsey Graham of South Carolina is getting campaign support from a third-party candidate, potentially bringing with him a narrow margin of conservative backers who could propel Graham over his Democratic challenger in a tightening race.

Bill Bledsoe, who had been running as the Constitution Party candidate seeking to block Graham from a fourth term, dropped out to endorse Graham, the Republican’s campaign told The Associated Press on Thursday.

“I appreciate Dr. Bledsoe’s support,” Graham said in a statement. “We agree on numerous issues like increasing the number of conservative judges on the bench, reducing the national debt, upholding the sanctity of life and having a strong military.”

According to its platform, The Constitution Party’s purpose is “to restore American jurisprudence to its Biblical foundations and to limit the federal government to its Constitutional boundaries.”

Bledsoe, a veterinarian from Spartanburg, ran against U.S. Sen. Tim Scott in 2016 as a fusion candidate of both the Constitution and Libertarian parties, hosting a series of “long-­gun carrying rallies” at courthouses around the state, carrying a Revolutionary War-era rifle to draw attention to gun restrictions.

In that contest, Bledsoe got 2% of votes cast.

Bledsoe said he appreciated Graham’s work on the judicial system the past four years.

“President Trump has asked that conservatives stand together and reelect Lindsey Graham in order to help make America great again, and I agree,” Bledsoe said.

Even a slim margin of support from ultra-conservatives could be just what Graham needs to win over Democrat Jaime Harrison.

During his three terms in the Senate, Graham has at times drawn criticism as not being conservative enough for the state, citing his willingness to work with Democrats to advance legislative goals. A close relationship with President Donald Trump, though, has helped to improve Graham’s standing in South Carolina, where Trump’s support remains strong.

“I know my race pretty well,” Graham said Thursday on Capitol Hill. “I think I will win decisively when it’s all said and done.”

Harrison has previously hinted that third-party candidates in the race could help him by siphoning support from Graham. A Libertarian candidate is also seeking write-in support in the general election.

In addition to tightening up, the race between Graham and Harrison has also shattered fundraising records, with both bringing in more than $30 million apiece throughout the race. They are set to meet in their first debate Saturday in Columbia.