WASHINGTON (AP) — A raucous public debate over the nation’s flawed immigration system is set to begin in earnest this week as senators finalize a bipartisan bill to secure the border, allow tens of thousands of foreign workers into the country and grant eventual citizenship to the estimated 11 million people living here illegally.

Already negotiators are cautioning of struggles ahead for an issue that’s defied resolution for years. An immigration deal came close on the Senate floor in 2007 but collapsed amid interest group bickering and an angry public backlash.

“There will be a great deal of unhappiness about this proposal because everybody didn’t get what they wanted,” Sen. John McCain, R-Ariz., a leader of the eight senators negotiating the legislation, said Sunday. “There are entrenched positions on both sides of this issue.”

“There’s a long road,” said Sen. Chuck Schumer, D-N.Y., appearing alongside McCain on CBS’ “Face the Nation.” ‘’There are people on both sides who are against this bill, and they will be able to shoot at it.”

Schumer, McCain and their “Gang of Eight” already missed a self-imposed deadline to have their bill ready in March, but Schumer said he hopes that this week, it will happen.

“All of us have said that there will be no agreement until the eight of us agree to a big, specific bill, but hopefully we can get that done by the end of the week,” said Schumer.

Schumer, McCain and other negotiators are trying to avoid mistakes of the past.

A painstaking deal reached a week ago knit together traditional enemies, the U.S. Chamber of Commerce and the AFL-CIO, in an accord over a new low-skilled worker program. The proposal would allow up to 200,000 workers a year into the county to fill jobs in construction, hospitality, nursing homes and other areas where employers say they have a difficult time hiring Americans.

The negotiators also have pledged to move the bill through the Senate Judiciary Committee and onto the floor according to what’s known in Senate jargon as “regular order,” trying to head off complaints from conservatives that the legislation is being rammed through.

A deal on immigration is a top second-term priority for President Barack Obama, and his senior adviser Dan Pfeiffer said Sunday that the bill being developed in the Senate is consistent with Obama’s approach — even though the Senate plan would tie border security to a path to citizenship in a manner Obama administration officials have criticized.

Pfeiffer didn’t answer directly when asked on “Fox News Sunday” whether Obama would sign legislation making a path to citizenship contingent on first securing the border. But he suggested Obama was supportive of the Senate plan.

“What has been talked about in the Gang of Eight proposal is 100 percent consistent with what the president is doing so we feel very good about it,” Pfeiffer said. “And they are looking at it in the right way.”

Sticking points remain. There’s still disagreement over plans for a new program to bring in agriculture workers, who weren’t included in the deal struck between the chamber and AFL-CIO. The agriculture industry is at odds with United Farm Workers over wages.

But overall, all involved are optimistic that the time is ripe to make the biggest changes to the nation’s immigration laws in more than a quarter-century. For many Republicans, their loss in the November presidential election, when Latino and Asians voters backed Obama in big numbers, resonates as evidence that they must confront the immigration issue.

“The politics of self-deportation are behind us,” said Sen. Lindsey Graham, R-S.C., referring to GOP candidate Mitt Romney’s suggestion in the presidential campaign. “It was an impractical solution. Quite frankly it’s offensive. Every corner of the Republican Party, from libertarians to the (Republican National Committee), House Republicans and the rank-and-file Republican Party member, is now understanding there has to be an earned pathway to citizenship.”

Graham and McCain also had praise for Sen. Marco Rubio, R-Fla., a member of the negotiating team who’s acted as a bridge to conservatives but also has kept advocates and other lawmakers guessing about whether he’ll ultimately support the bill.

“Marco Rubio has been a game changer in my party. He will be there only if the Democrats will embrace a guest worker program and a merit-based immigration system to replace the broken one,” Graham said on NBC’s “Meet the Press.”

After consideration by the Judiciary Committee, floor action could start in the Senate in May, Schumer said.

Meanwhile two lawmakers involved in writing a bipartisan immigration bill in the House, Reps. Luis Gutierrez, D-Ill., and Mario Diaz-Balart, R-Fla., sounded optimistic that they, too, would have a deal soon that could be reconciled with the Senate agreement.

“I am very, very optimistic that the House of Representatives is going to have a plan that is going to be able to go to a conference with the Senate in which we’re going to be able to resolve this,” Gutierrez said Sunday on CNN’s “State of the Union”.