The bill would allow police to check the immigration status of any person they believe might be in the country illegally.
Most folks we talked to think there need to be tougher laws to keep illegal immigrants out.
"It's over-burdening the United States. We got to worry about our Social Security. Now they want to give Social Security to the ones that aren't even allowed to be here," said Cecil Cassatt of Myrtle Beach.
"If you're illegal then no, you shouldn't be here. They should definitely crack down on it, I think so," added Rico Hinson of West Columbia.
But Peggy Ryals, who teaches English to immigrants in Myrtle Beach, says South Carolina already has a tough immigration law, passed in 2008.
She says the state doesn't need a new law that would cost millions to enforce.
"And if we pass it, where are we going to detain them? Who's going to build the detention centers? We are, with tax dollars that need to go to the schools," Ryals said.
Sen. Grooms told a Greenville newspaper that to protect people in South Carolina, he wants the state to do all it can to have the smallest illegal immigrant population in the country.
But even those who want tough immigration laws, aren't sure that a law crafted after the one in Arizona is what South Carolina needs.
"I really think that Arizona went over the hill a little bit too far, but I do think there ought to be very good immigration laws that are enforced," said George Jenkins of Myrtle Beach.
A new report from the Pew Hispanic Center says the number of illegal immigrants in South Carolina dropped more than 20 percent over the past 3 years.
Grooms says the 2008 law may be one reason for the drop, but he wants the number to go down even more.