The broad agreement on a need for immigration changes and a pathway to citizenship for an estimated 11 million illegal immigrants already here is driven largely by self-interest. Both business and labor see an overhaul of the nation’s broken immigration system as a way to boost economic competitiveness with other nations while increasing the ranks of workers and union members.

For President Barack Obama, a partnership between factions that have often been at odds — both with each other and with the White House — allows him to turn up pressure on Congress and try to isolate congressional Republicans who oppose parts of an immigration overhaul. Obama held separate private meetings at the White House on Tuesday with labor leaders and top business executives.

“This is all very encouraging to have labor and business come together to explore what could be some common ground,” said Janet Murguia, president of the National Council of La Raza, a leading immigrationrights groups. Murguia and other immigration activists joined Obama’s meeting with labor groups.

Despite such optimistic public statements, the fragile business-labor alliance is still in question as the Chamber of Commerce meets with the AFL-CIO and other labor groups privately to hammer out details of how to deal with future immigrants who come to the U.S. to work. The labor and business groups have been tasked by Sen. Charles Schumer, D-N.Y., with reaching a deal within weeks that can be included in legislation being crafted by a bipartisan Senate group, officials say.

The guest worker issue helped scuttle the last attempt at a comprehensive overhaul of immigration law in 2007. If the parties can’t reach a deal, senators and their staffs are prepared to write temporary-worker language themselves, said a Senate aide, who spoke only on condition of anonymity because the aide was not authorized to discuss the private negotiations publicly.

The Senate negotiating group has included a guest-worker program in its immigration proposals, but Obama has not. That omission has drawn criticism from Sen. Marco Rubio of Florida, a key negotiator on the Republican side. Republicans view the omission as a cave-in to labor supporters, who see a substantial new guest-worker program as a possible threat to Americans who are seeking jobs.

White House officials say the president is open to a guest-worker program, so long as it protects workers and responds to workforce demands, not politics. That puts the White House in line with AFL-CIO president Richard Trumka, who said following his meeting with Obama on Tuesday that they discussed “a data-driven system that is actually driven by needs and not by aspirations of employers.”

Even if overhaul legislation makes it through the Senate, trouble lies ahead in the Republican-controlled House.

The chairman of the House Judiciary Committee said Tuesday the nation’s immigration system is “in desperate need of repair” as he opened an overhaul hearing. But he also said there are many questions about how any large-scale legalization program would work, how much it would cost and how it would prevent illegalimmigration in future.

The chairman, Rep. Bob Goodlatte of Virginia, questioned whether another approach besides citizenship might be possible: “Are there options we should consider between the extremes of mass deportation and a pathway to citizenship for those not lawfully present in the United States?” he asked.

Obama has found himself at odds with both business and labor during his first term. Business leaders, in particular those representing Wall Street banks, recoiled at the president’s financial regulation law and his labeling of bankers as “fat cats.” Labor unions opposed Obama’s pursuit of free trade agreements, as well as his decision to hold his party’s convention last summer in North Carolina, a right-to-work-state that makes it more difficult for unions to organize.

By bringing both factions together to support one of the president’s top second-term priorities, the White House sees an opportunity to pressure Republicans to back the president — and set the GOP up to carry the blame if the current negotiations fail.

Underscoring the risk for Republicans, House Majority Leader Eric Cantor, R-Va., on Tuesday embraced “an opportunity for legal residence and citizenship for those who were brought to this country as children and who know no other home.” It appeared to be a change for Cantor, who voted against DREAM Act legislation to allow a path to citizenship for certain immigrants brought here as youths.

The guest worker program addresses what’s called “future flow” — the influx of migrants to the U.S. that’s sure to come whether or not Congress passes an immigration bill.

If Congress does act to provide a pathway to citizenship for the estimated 11 million illegal immigrants now in the country, it’s just as important to deal with future immigration, advocates say. Otherwise, the country will again find itself home to many illegal immigrants. A major criticism of the 1986 immigration law signed by President Ronald Reagan, which offered legalization to some 3 million illegal immigrants, was that it did not deal with the issue of future immigration — allowing today’s problems to emerge.

In 2007, comprehensive immigration legislation foundered after an amendment was added to end a temporary worker program after five years, threatening a key priority of the business community. The amendment passed by just one vote, 49-48. Obama, a senator at the time, joined in the narrow majority voting to end the program after five years.

The U.S. does have several temporary worker programs already, but they’re viewed as cumbersome and outdated, and experts say a large proportion of migrant workers in agricultural and other low-skill fields like landscaping or housekeeping are in the U.S. illegally.

For business and labor, the question is how to come to an agreement on how many workers to let in, under what circumstances and how much they would be paid. Another key issue: whether and how they would be able to attain eventual permanent residency, the critical step toward citizenship.

“We have to get to the question of what is the structure for the future and what rights do the workers that get here in the future, what rights do they have,” said Eliseo Medina, secretary treasurer of the Service Employees International Union.

For business groups, a temporary worker program is a key piece of any immigration legislation.

“It’s not as if employers want to hire guest workers. We want to hire Americans. It’s only when we can’t find them that we hire the guest workers,” said Shawn McBurney, senior vice president of government affairs at the American Hotel and Lodging Association.

The Senate aide said that lawmakers are eyeing somewhere in the range of 200,000 to 400,000 visas for low-skilled temporary workers, including for agriculture and non-agriculture. Unlike in current programs, negotiators are also eyeing ways to peg the numbers to labor market demands. Employers would have to show they could not find American workers for the jobs.

The nonpartisan Migration Policy Institute and others have proposed the creation of a permanent commission that would make recommendations about where and when workers are needed, an idea said to be under consideration as the business and labor groups negotiate. However, business groups are skeptical of the idea.