Collins said Homeland Security Secretary Michael Chertoff told her of the impending veto threat.
A White House spokesman did not immediately respond to a request for comment.
Such a veto threat would be an effort to flex Bush's political muscle with the new, Democratic-led Congress on the old battleground of labor rights. It also could throw an obstacle into talks over how to debate and pass the recommendations of the Sept. 11 Commission.
For now, senators are eager to follow the House and pass a bill enacting the commission's recommendations to tighten the nation's security. The House bill also includes a provision that would let TSA screeners bargain collectively.
Senate Majority Leader Harry Reid of Nevada and Republican leader Mitch McConnell of Kentucky had reached a tentative agreement Tuesday to conduct the debate over the next 10 days without the distraction of Iraq.
The sense of urgency on the 9/11 recommendations was conveyed to both leaders in a letter Tuesday from families of those killed in the terrorist attacks on that day in 2001.
"This legislation is far too important to be politicized by - controversial amendments and debate, particularly those relating to Iraq," wrote Carol Ashley and Mary Fetchet of the Voices of September 11th.
Reid and McConnell said the Iraq debate would wait for next month, after passage of the 9/11 bill. The arrangement would allow the Senate to debate legislation bolstering antiterrorism security measures on railroads and airlines without being distracted by the furor over President Bush's buildup of troops in Iraq.
"We have got to finish this bill," Reid, D-Nev., said as he opened the Senate session. He read parts of a letter from relatives of people killed in the Sept. 11, 2001 terrorist attacks asking the Senate to consider the legislation "without complications regarding Iraq."
Even minus an Iraq debate, provisions in the antiterrorism bill or planned amendments make the legislation contentious.
The administration vigorously opposes a measure that would give TSA screeners the same collective bargaining and whistleblower rights held by most other federal employees. The White House also opposes an amendment that would let states delay adopting standardized drivers' licenses.
Senate Homeland Security Committee Chairman Joe Lieberman of Connecticut said screeners have been denied the most basic employee protections since joining the federal payroll after the Sept. 11 attacks.
Collins said Chertoff delivered a staunch defense of the administration's position during the GOP caucus' weekly policy lunch Tuesday. She said she nonetheless plans to try to attach an amendment that would delay requirements for states to adopt national drivers license standards.
Many states have complained about the cost of the program, and civil libertarians are concerned about privacy issues.
Other measures in the bill would improve rail and aviation security, provide funds for state and local emergency communications systems, improve intelligence sharing between federal, state and local officials, and expand a visa waiver benefit for favored countries.
The bill is S.4