U.S. businesses would be allowed to hire 20,000 foreign workers for low-skilled jobs in the first year of a new visa program being developed by a bipartisan Senate group — a figure that would rise slowly to a maximum of 75,000 in 2020, people with knowledge of the proposal said Friday.

As the senators continued to negotiate details of the program to break an impasse between labor and business leaders, those familiar with the talks said it would take many years before the visa program would approach the annual proposed cap of 200,000 foreign workers.

Meanwhile, construction industries would be severely limited under the plan, allotted no more than one-third of the new visas. Those companies also would be banned from hiring any foreigners for higher-skilled technical jobs such as electricians, said the sources, who spoke on condition of anonymity to disclose private talks. The AFL-CIO has pushed hard to keep strict limits on construction companies from hiring foreigners.

The limit on construction visas remained a hurdle late Friday for the group of eight senators as it attempts to craft final agreement on the guest-worker program that would win support from the varied interests in the business community. Republican members of the Senate working group were continuing to push to win more slots for foreign construction workers, the sources said.

“We are very close, closer than we have ever been, and we are very optimistic, but there are still a few issues remaining,” Sen. Charles E. Schumer (D-N.Y.), a member of the Senate group, said in a statement Friday.

Despite Schumer’s optimism, union and business leaders have proclaimed previously that they have been in harmony. The sides released a joint statement of shared principles in February, but talks broke down late last week over the details of the guest-worker program. That forced the eight senators involved in the bipartisan talks to miss a self-imposed deadline of March 22 to have a final agreement on a comprehensive immigration bill that is expected to feature a path to citizenship for the nation’s 11 million illegal immigrants.

Both labor and business said progress has been made on the other major sticking point of the guest-worker program, with both sides agreeing to a wage scale that would pay foreigners the greater of actual or prevailing wages. That would be based on a formula that takes into account actual wages paid by the employer to similarly situated U.S. workers as well as regional and industry scales.

Businesses have lobbied for 400,000 new visas under the new program, but labor unions want far fewer because of concerns that such a system would negatively affect wages and benefits for American workers. Though the program would start at 20,000 visas in its first year, it would grow based on recommendations from a new federal bureau that would analyze employment data.

Under the proposal that is being developed, businesses would be allowed to hire additional workers in a given year beyond the annual cap — but those workers would be paid a far higher pay rate that could be up to 70 percent higher than the prevailing wages, the people familiar with the plans said.

Construction companies, however, would not be allowed to hire any additional workers above the program cap, even if they were willing to pay more.

The construction industry has pushed back hard against the low caps, lobbying the Republican members of the Senate group to try to win more slots from their Democratic counterparts, the sources said.

“Ultimately, the final decisions will be made by the senators involved,” Chamber of Commerce senior vice president Randel Johnson said in a statement.

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