Gov. Nathan Deal on Wednesday said that lawmakers struggling to adopt illegal immigration legislation are tackling an increasingly difficult subject, but he refrained from offering advice.

Deal, speaking to reporters at the Capitol after an economic development announcement, said immigration is a sticky wicket.

"It's an issue that the public of Georgia expects us to deal with, even though we have one of the more comprehensive bills already in place as a result of the legislation several years ago," Deal said.

The House on Tuesday rejected a Senate immigration plan for its own, more stringent version. The bill, House Bill 87, was sent back to the Senate, which failed to act on it before adjourning for the day. The General Assembly reconvenes Thursday for the final day of its 40-day session.

Deal said his staff has been "in consultation" with lawmakers, "but I view this as primarily a legislative responsibility. The difficulty they have encountered reflects the complexity of the issue, and certainly it's a very multifaceted issue and a difficult one to come to logical conclusions that will be meaningful."

The House version of the bill requires private businesses with more than 10 employees to use a federal work authorization program called E-Verify. The Senate stripped a similar provision out of the bill after nearly three hours of debate and several votes on amendments Monday evening.

On other issues, Deal said he has no timeline to sign Senate Bill 10, which would allow local governments to hold referendums on whether to allow the sale of alcohol in stores on Sundays. The bill received final approval in the House late Tuesday.

Deal, while saying he would vote against legalizing Sunday sales in his own community, said he won't tell local governments what to do.

"We just give them the option to do that," he said. "I certainly do not encourage them one way or another. I view this as an issue that local government has a better feel for."