Washington (CNN) -- With Arizona's controversial immigration law set to go into effect next month, calls for federal action on comprehensive immigration reform are growing louder.
But with other issues dominating Congress' schedule, can the bill currently in the House gain any traction?
Yes, according to a leading Hispanic congressman involved in the immigration reform fight.
"We know the legislative clock is ticking. We know people are getting deported at the highest rate in modern history," Rep. Luis Gutierrez said in remarks delivered at a news conference Thursday, attended by dozens of members of Congress. "We know that the Arizona law, which, unless something happens, will go into effect in about one month, is a call to action. It is a cry of frustration."
Arizona's law, signed by Gov. Jan Brewer in late April, requires police to question people about their status if they have been detained for another reason and if there's reason to suspect they're in the United States illegally. It also targets those who hire illegal immigrant laborers or knowingly transport them.
More than a dozen states are now following Arizona's lead in taking up legislation to deal with illegal immigration.
Gutierrez, a Democrat from Illinois and chairman of the Immigration Task Force of the Congressional Hispanic Caucus, said July will be a critical month in getting the House's Comprehensive Immigration Reform for America's Security and Prosperity Act on the front burner. The bill has more than 100 co-sponsors.
"After the August recess, we all know the chances of major action dwindle and that if the Arizona law is allowed to go into effect, it will cause massive disruptions and set a dangerous precedent," he said.
Gutierrez believes that an immigration bill can be passed this year with bipartisan support from both legislative chambers, according to Gutierrez spokesman Douglas Rivlin.
"He has offered to bring 200 House Democrats to the table if the House Republicans can bring 20 and the math is similar in the Senate," Rivlin said. "He would not be pushing it if it were impossible."
On the Senate side, Sens. Chuck Schumer, D-New York, and Lindsey Graham, R-South Carolina, have an immigration plan of their own, which was introduced in March.
"The American people deserve more than empty rhetoric and impractical calls for mass deportation," the two senators said in a March 19 Washington Post op-ed. "We urge the public and our colleagues to join our bipartisan efforts in enacting these reforms."
So far, the legislative plan has failed to gain traction and will probably be pushed aside as the Senate tackles the Supreme Court confirmation hearings and other issues such as financial regulatory reform.
Obama, though, has signaled that he is hopeful the senators' plans will gain momentum.
But it's not just members of Congress pushing for federal action.
Homeland Security Secretary Janet Napolitano recently said that Congress should move on legislation while the administration strengthens security at the U.S.-Mexican border. She said it's the federal government's job to set immigration and border security policies.
"We need a single, functional immigration and border policy," she said. "We cannot have 50 different state policies. It simply will not work for us."
Case in point, advocates say: Voters in Fremont, Nebraska, passed a much-debated measure Monday that would prohibit businesses and landlords from hiring or renting to people who are in the United States illegally.
Ali Noorani, executive director of the National Immigration Forum -- a leading immigrant advocacy organization -- said in a statement Thursday that allowing states to create their own legislation would "create chaos and confusion for both immigrants and law enforcement while not fixing the immigration problem at its core."
"We don't need an uneven patchwork of state-based immigration laws; we need a comprehensive national solution," Noorani added. "State-based immigration proposals should be a wake-up call to Congress, they need to take the steering wheel, fix the immigration problem and finally pass comprehensive immigration reform."
Advocates for immigration reform legislation point to polls showing that Americans are not only concerned about the issue, but want federal action now.
In late May, a CNN/Opinion Research Corp. poll showed that six in 10 respondents found that the federal government should focus on stopping the flow of illegal immigrants into the U.S., deporting those already here and supporting more border security.
An ABC News/Washington Post poll released in mid-June found that 52 percent of respondents said immigration enforcement should be under the control of the federal government, and 46 percent said immigration laws should be made and enforced by the states.
CNN's Carol Cratty contributed to this report.