Democrats and immigration advocates have termed the Cornyn amendment as "poison pill."

While acknowledging Cornyn had "ratcheted" up matters, Shotwell said she remained optimistic reform would happen.

"Both parties recognize this is a problem we have to solve," she said. "I think the Senate will work out something."

She and Aitken agreed the odds of adoption of comprehensive reform – contained in an 867-page overhaul that has so far made it out just one House committee – seem better than they have in years.

"This is the best time since 1986 that we will have the opportunity to reform our nation's immigration laws," said Aitken, VP of government affairs for SHRM.

A final vote in the Senate is set to come by the time senators leave for their Fourth of July break. Failing that, there's nothing stopping lawmakers from picking up the debate when they return or, as Aitken pointed out, in 2014, when midterm elections are scheduled. The biggest reforms on immigration in recent decades have typically won passage during election years, he noted.

The legislation was drafted in the same spirit of compromise that will be required in the days ahead if it's to get through Congress.

Shotwell predicted that failure to get the legislation through will hurt American workers, as well as those who hope to immigrate to the U.S. by obtaining a green card.

If nothing happens in Washington, she said, employers wanting to expand their operations will likely do so in other countries, where they can find the skills they need to operate their plants.

"They need assurance they can find the talent they need," Shotwell said. "This legislation provides that."

Provisions in the legislation to expand the number of specialized visas issued to highly skilled workers – typically those in the technology industry – also are of critical importance to employers, she said.

"We put our nation at a competitive disadvantage," if Congress fails to pass reform, she said. "The government has to find a new way of doing business."

Beyond boosting employment-based green cards and visas, SHRM and ACIP, which is an affiliate of the organization, have been pushing for the creation of a Trusted Employer program and the establishment of a single, national and entirely electronic employment verification system.

Trusted Employer would work along the lines of Trusted Shipper, Trusted Traveler and TSA Pre-Check, allowing the government to pre-qualify employers with a proven track record of compliance with federal immigration laws. The program would streamline the processing of petitions.

Companies that routinely hire foreign nationals would see the greatest benefits.

Trusted Employer would help offset one of the biggest problems now seen in the current E-Verify system: fraudulent Form I-9 paperwork, too often obtained with false or stolen identification.

"E-Verify … does a lot of things well," Aitken said. "One of the things it doesn't do well, however, is tell you if the individual standing in front of you presenting work authorization and identity documents actually owns the identity on those documents."