WASHINGTON – Republicans and Democrats working to push through a broad immigration measure are weighing a bargain that would trade a tougher legalization road for millions of unlawful immigrants for a better deal for family members of U.S. citizens and permanent residents.

The swap under discussion among senators and the White House could essentially neutralize proposals from opposite sides of the political spectrum that are seen as potentially fatal changes to the bipartisan deal. Congressional aides in both parties described the idea on condition of anonymity because the talks were continuing.

It was just one element of an intense round of horse-trading going on behind the scenes as lawmakers worked to complete the controversial measure.

Sen. Kay Bailey Hutchison, R-Texas, wants to require all heads of households of illegal immigrant families to return home before gaining lawful status _ not just those seeking green cards, as the bill dictates.

Sen. Robert Menendez, D-N.J., wants to allow hundreds of thousands of people who had applied for permanent legal status by the beginning of the year to get green cards based purely on their family connections _ a preference that the bill ends for most relatives who got in line after May 2005.

Congressional and White House officials have been working to strike a compromise that would allow votes on both as early as Tuesday, with the goal of bringing key Republicans and Democrats on board to support the final bill.

The so-called “Gang of 12” critical players who crafted the deal was to meet Tuesday to discuss the potential trade and to plot how to handle other major revisions that could otherwise sink their agreement. It will be their first confab since lawmakers returned from a weeklong break where the measure was a hot topic among constituents.

The bill is facing its steepest challenges yet this week, including a Republican effort to strictly limit the illegal immigrants to whom it would award lawful status.

Top aides in both parties expect a close vote on a proposal by Sen. John Cornyn of Texas to bar illegal immigrants who have defied deportation orders from gaining legal status.

They’re also concerned about Democratic efforts to give family connections higher priority in the measure, which for the first time evaluates future arrivals more on education, skills and job experience than on blood ties.

In addition to Menendez’s proposal, several Democratic presidential hopefuls have proposed family-related changes.

Sen. Hillary Rodham Clinton, D-N.Y., is proposing allowing more spouses and minor children of legal permanent residents to immigrate to the U.S., by exempting them from visa caps.

The Senate also is considering a bid by Sen. Christopher Dodd, D-Conn., to more than double, to 90,000 a year, the number of green cards available for parents of U.S. citizens.

Sen. Barack Obama, D-Ill., plans an attempt to phase out the point system that gives little credit for family ties to a U.S. citizen or permanent legal resident.

Sen. Edward M. Kennedy of Massachusetts, the lead Democratic negotiator on the measure, is sympathetic to the family changes but concerned that adopting them could cost the bill vital support, aides say.

Sen. Jon Kyl, R-Ariz., another architect of the bill, has made ending so-called “chain migration” – immigration based largely on family ties – a top priority. He described the proposals by Menendez and Clinton as “killer amendments” whose passage would prompt him to “do everything I could to get (the bill) defeated.”

Still, Cornyn has said he is inclined to back Menendez’s proposal, since it would give people who have applied for green cards an advantage over those who came to the U.S. illegally.

If accepting it would pave the way for toughening the legalization process – such as by broadening the group of illegal immigrants who must return home or requiring them to do so sooner – then even more Republicans might be able to be brought along.

The measure requires that illegal immigrants seeking green cards wait until an approximately eight-year backlog is cleared before applying, and that heads of household go home to do so. Negotiators have discussed moving up the requirement so that they would have to return home sooner, within two or four years.

The so-called “touchback” requirement, once considered anathema by Democrats, is a key element of the compromise and – along with steep fines for illegal immigrants – a major reason that President Bush and Republican supporters argue the measure’s grant of legal status doesn’t amount to amnesty.