Thomson Reuters
Senator Lindsey Graham speaks at the First in the Nation Republican Leadership Conference in Nashua.
"I worry a lot about the GOP," Graham told "Fox & Friends."
The South Carolina senator continued: "I worry that the GOP is cutting its own throat by doubling down on the idea that we're gonna deport all illegal immigrants including grandmothers who have done nothing but be here to have tried to earn a life."
Donald Trump, the presumptive Republican nominee for president, has repeatedly called for an indefinite ban on Muslim immigration and said the millions who live in the US illegally need to be deported.
In the interview, Graham also offered another reason he has yet to throw his support behind Trump.
"I'm gonna make a decision what I think is best for this country. He won 32% of the vote in South Carolina. I'm not going support Hillary Clinton or Donald Trump because I don't believe either one of them have a plan to keep my country safe," Graham said, referring to each candidate's national-security plan.
Graham said he was "so sorry we are where we are" in the 2016 election.
The senator launched what ended up being a failed bid for president in 2016. He dropped out of the race in December saying he "hit a wall" in the campaign.