Supporters of a tenuous immigration overhaul today beat back an attempt to deny millions of illegal immigrants who have violated deportation orders the right to stay in the country.

By 46-51, the Senate rejected the amendment by John Cornyn, R-Texas, that was considered a deal breaker by the Republicans and Democrats who negotiated the comprehensive immigration overhaul with the White House.

Minutes before, the chamber adopted 66-32 an alternative amendment by Massachusetts Sen. Edward M. Kennedy, the Democrats’ chief negotiator.

Kennedy’s amendment included elements of the Cornyn amendment that barred immigration benefits to members of terrorist-related organizations, known gang members, sex offenders, alien smugglers who use firearms and felony drunk drivers.

But Kennedy said Cornyn’s broader amendment could have disqualified many illegal immigrants who had used false documents and potentially could gut the bill’s contentious legalization component.

Cornyn said the legislation (S 1348) leaves a “big gaping hole for those who showed nothing but contempt for our laws.”

At midday, Senate leaders were busy working to allow votes on a dozen or so additional amendments, but had not yet reached an agreement leading to a final passage vote on the bill.