WASHINGTON (AP) ― A noisy debate over the flawed U.S. immigration system will 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.

Negotiators warned of struggles ahead, but all involved are optimistic that it’s time to make the biggest changes to the nation’s immigration laws in more than a quarter-century.

“There will be a great deal of unhappiness about this proposal because everybody didn’t get what they wanted,” Republican Sen. John McCain, a leader of the eight senators negotiating the legislation, said Sunday on CBS.

Democratic Sen. Chuck Schumer, another of the eight senators involved, told CBS he’s hoping for a bipartisan deal by the end of this week.

In a bitterly divided Congress, the immigration bill appears to be one of the few major pieces of legislation that is likely to receive bipartisan support and become law. For many opposition Republicans, their loss in last year’s presidential election, when Latino and Asians voters backed President Barack Obama in big numbers, resonates as evidence that they must confront the immigration issue.

“Every corner of the Republican Party ... is now understanding there has to be an earned pathway to citizenship,” Republican Sen. Lindsey Graham said.

A deal on immigration is a top priority for Obama in his second term, and senior adviser Dan Pfeiffer said Sunday on Fox that the bill being developed in the Senate is consistent with Obama’s approach. He didn’t answer directly when asked whether Obama would sign legislation making a path to citizenship contingent on first securing the border.

Obama has stressed that a path to citizenship should not have major hurdles, and some immigration advocates believe that’s what a requirement for a secure border would amount to.

But Republicans involved in the Senate negotiations have made clear that border security is a must for them before those living here illegally can be allowed to move toward citizenship.

“We are going to secure that border and it will be tied to a pathway to citizenship or there will be no deal,” Graham said.

Graham also suggested that disagreement over a new low-skilled worker program could still be hanging up an overall immigration deal ― even after an agreement a week ago between the AFL-CIO labor federation and the U.S. Chamber of Commerce, an influential pro-business lobbying group.

The hard-won deal between labor and business would ultimately allow up to 200,000 workers a year into the U.S. to fill jobs in construction, hospitality, nursing homes and other areas where employers now say they have a difficult time hiring Americans or legally bringing in foreign workers. Even after the deal was struck, some industries, such as construction, continued to voice complaints about the terms.

Without offering details, Graham said on NBC that negotiators were revisiting the low-skilled worker deal. But he issued a statement a short time later saying he was confident the agreement would hold.

Graham sounded optimistic overall, predicting the bill would pass the 100-member Senate with 70 votes in favor. Senators believe an overwhelming bipartisan vote is needed in the Democratic-led Senate to ensure a chance of success in the Republican-controlled House of Representatives.

Floor action could start in the Senate in May, Schumer said.