Hundreds of protesters participated in the two-mile march in Chicago on May 1. The majority of the marchers were protesting for immigration reform. (Scott Olson/Getty Images)

The Senate opened floor debate Friday on a bipartisan proposal to overhaul immigration laws, kicking off a process that chamber leaders hoped would result in a vote on the comprehensive legislation before July 4.

“The vast majority of American people want us to move forward on this,” Majority Leader Harry M. Reid (D-Nev.) said as he made a motion to proceed with the bill.

Referring to opponents of the bill, who have sought to delay deliberations with dozens of amendments, Reid added, “Sometimes in the process we have here, people throw monkey wrenches in, and we can’t move forward as fast as we want.”

Leading critics took to the floor to begin making their case against the proposal, which features a 13-year path to citizenship for immigrants who entered the country illegally, new visas for high-tech and low-skilled workers, increased border security investments and the elimination of some categories of visas for extended family members.

Sen. Jeff Sessions (R-Ala.) denounced the bill as being written in secret by a small group of senators — four Democrats and four Republicans — that negotiated with labor unions, the U.S. Chamber of Commerce, tech companies and pro-immigration groups.

Sessions said the legislation would allow up to 11 million illegal immigrants to gain legal status before ensuring that the U.S. border with Mexico is secured.

“The legislation offered by the ‘Gang of Eight’ says they fixed it. ‘Don’t worry. We’ve taken care of all that is needed. We have a plan that will work in the future and end the illegality,’ ” Sessions said of the bipartisan group. “Well, it won’t do that. That’s the problem. It will definitely give amnesty today, immediate legal status for 11 million people today. But the policies of enforcement for the future . . . are not fulfilled in this legislation.”

The Senate is expected to vote on the motion to proceed early next week, and Republican leaders, including Minority Leader Mitch McConnell (Ky.), have said they will not stand in the way of the bill proceeding to the floor. President Obama, who has supported the bipartisan bill, is scheduled to make remarks about the legislation Tuesday at the White House.

Some proponents of the legislation have said that they are confident they can win the 60 votes needed to prevent a filibuster and that they are seeking to get as many as 70 to put political pressure on the GOP-controlled House. But Sen. Marco Rubio (R-Fla.), a member of the bipartisan group, has said he does not believe the Senate bill could pass either chamber without significantly strengthening border security measures.

House leaders have said they will proceed with their own immigration bill. A bipartisan House group negotiating a comprehensive package has failed to reach an agreement after months of talks.

The tough path for immigration was highlighted Thursday when House Republicans voted to halt the Obama administration’s policy of deferring deportation of young adults brought to the country illegally as children.

The 224 to 201 vote, which broke along party lines, was an ominous sign for reform efforts. Efforts to normalize the status of so-called “Dreamers” have been among the most popular parts of changes to immigration law.

To qualify for deferred deportation under Obama’s policy, young adults had to have come to the country before the age of 16 and be high school graduates or have served in the military. They must have clean criminal records.

Republicans have opposed the policy since Obama introduced deferred deportations in June 2012, arguing that he overstepped his authority.

The House vote provoked backlash among immigrant groups that Republicans have sought to woo since Obama won more than 70 percent of the Latino vote in the 2012 election.

“This is an outrage and the exact opposite of what our country needs from its political leaders,” said United We Dream Managing Director Cristina Jimenez, who warned that Republicans were at risk of sealing their fate “as an out-of-touch, extremist party that has forever marginalized the immigrant and Latino community.”