Atlanta (CNN) -- After supporters and critics of Georgia's controversial new immigration measure faced off in federal court Monday, a judge said he hoped to weigh in on the law by next week.

U.S. District Judge Thomas Thrash Jr. said he intended to issue a written ruling before July 1, when the law is scheduled to go into effect.

Attorneys representing plaintiffs in the class-action suit against the law asked Thrash to issue a temporary injunction that would stop the law, known as HB 87, while the court considers the case.

Attorneys representing the state filed a motion to dismiss the class-action suit.

"HB 87 is deeply flawed and fundamentally unconstitutional," said Omar Jadwat, an attorney for the American Civil Liberties Union.

Immigration laws are the U.S. government's responsibility, he argued.

"It's not for Georgia to make the decision that federal law is insufficiently harsh," he said.

The state law, which is aimed at cracking down on illegal immigration, allows police to ask about immigration status when questioning suspects in certain criminal investigations.

It also allows the imposition of prison sentences for people who knowingly transport illegal immigrants during the commission of a crime and says that workers convicted of using fake identification to get jobs could be sentenced to 15 years in prison and fined $250,000.

"Sometimes the law is harsh, there's no question about that, but that doesn't make it unconstitutional," said Devon Orland, senior assistant attorney general for the state.

Thrash questioned Orland throughout the two-hour hearing, repeatedly asking the attorney to clearly define the purpose of the law.

"Don't you concede that this provides local law enforcement with a tremendous amount of discretion?" he asked.

Orland compared the new immigration measure to provisions that allow local authorities to make arrests using federal laws in drug and weapon cases. She argued the law mirrors federal immigration regulations and clarifies the role that local law enforcement plays in enforcing them.

But Thrash said the law appeared to give local governments too much leeway.

"You're going to have 159 different versions, because every county and municipality will have its own interpretation of the law," he said.

Economic issues also figured prominently in Monday's hearing.

Orland argued that money was one of the main motivations of Georgia's law, saying illegal immigrants were using state resources.

"The federal government simply can't be everywhere ... and it is costing the state of Georgia an extraordinary amount of money," she said.

In his questioning, Thrash alluded to contributions immigrants make to the state's economy, and said the law could open the door to selective enforcement.

"We like the people at the restaurant. Let's not bother the cook or the guy that does the mayor's yard work. They're a nice family. But we're going to make it so difficult for everybody else they're going to leave," he said.

Orland countered that Georgia's reliance on immigrant labor was not a legal consideration.

"Let's not forget, just because we're economically dependent on something unlawful, doesn't change it to being lawful," she said.

As attorneys made their arguments, a small group of protesters rallied outside the federal courthouse in downtown Atlanta, chanting, "What do we want? Injunction! When do we want it? Now!"

Fear kept more people from participating in the demonstration, protest organizer Adelina Nicholls said.

"People have been scared, absolutely," said Nicholls, the executive director of the Georgia Latino Association for Human Rights. "That's the climate we're living in -- people feel they have a right to ask you for your papers."

Nicholls said she fears the law will increase profiling of Hispanics, but attorneys representing the state said the concerns are unfounded.

"Any such fear is purely hypothetical and speculative in light of the clear terms of HB 87 that prohibit unconstitutional racial profiling and require criminal conduct before any verification of immigration status would enter the realm of possibility," says the attorneys' brief supporting their motion to dismiss the case.

The Georgia Attorney General's Office declined to comment further after the hearing, a spokeswoman said.

Jadwat, the ACLU attorney, said he was "positive and hopeful," even though the judge did not make a ruling.

The ACLU, the National Immigration Law Center, the Southern Poverty Law Center and the Asian Law Caucus are representing plaintiffs in the Georgia lawsuit.

Several organizations, including the Anti-Defamation League and the American Immigration Lawyers Association, have filed friend-of-the-court briefs supporting the lawsuit. The governments of 12 Latin American countries also filed friend-of-the-court briefs, saying the law will negatively impact their relations with the United States and people of Latin American descent in Georgia.

The Georgia lawsuit is the latest battle in a nationwide skirmish between state and federal officials over who controls immigration enforcement.

Arizona's controversial law aimed at cracking down on illegal immigration catapulted the issue onto the national stage last year, drawing a lawsuit from the U.S. Department of Justice, which argues the law is unconstitutional.

In April, a three-judge panel on the 9th U.S. Circuit Court of Appeals sided with the Justice Department and against Arizona Gov. Jan Brewer, who signed Arizona's law last year. Brewer announced last month that the state would appeal directly to the U.S. Supreme Court.

The Justice Department has not joined the Georgia lawsuit.

In Monday's hearing, Thrash referred to the Justice Department's involvement in the Arizona legal battle. Orland said the Arizona statute is "quite a bit different" than the Georgia law.

CNN's Gustavo Valdes contributed to this report.