WASHINGTON -- The Senate approved broad legislation Tuesday to give state and local governments new weapons to stop terrorists intent on destruction within U.S. borders.

But more than five years after the Sept. 11 attacks, the bill still faces considerable hurdles. Differences remain with legislation the House passed in January, and the White House threatened a veto over a provision to give airport screeners limited bargaining rights.

Tuesday's Senate vote was 60-38. Washington's Democratic Sens. Maria Cantwell and Patty Murray voted for the bill.

The new Democratic majority made the legislation one of its most urgent tasks, saying it was long past time to carry out the July 2004 recommendations of the bipartisan 9/11 commission formed after the 2001 attacks.

"This bill is a direct response to the appeals of the 9/11 Commission and the 9/11 families to take constructive action," said Sen. Joe Lieberman, I-Conn., co-sponsor of the measure.

The bill would approve $3.1 billion in each of the next three years for first-responder grants to the states while adjusting the formula on how the money is divided among high-risk states and states less vulnerable to terrorist attacks. Of that, $1.3 billion is specified for high-risk urban areas.

It would create an emergency communications grant program, funded at $3.3 billion over five years, require bags checked on planes to be screened with the same aggressiveness as carry-ons and outline rail and transit security improvements.

The House bill, passed in the first week of the new Congress, would require, within five years, 100 percent radiation scanning of all cargo-ship containers loaded at foreign ports and inspection of all cargo on passenger planes within three years.

An amendment to the Senate bill, offered by Sen. Robert Menendez, D-N.J., directs the Department of Homeland Security to come up with a plan, with yearly benchmarks, that leads to 100 percent scanning of cargo containers entering U.S. ports.

The Senate bill would move to block potential terrorists from entering the country by improving reporting of lost or stolen passports and requiring countries to provide information about visitors who could pose a threat to the United States.

The two bills also differ on how security grants would be distributed among the states. The House bill would favor high-risk states such as New York and California, while the Senate, where small-state lawmakers have more sway, would divide the money more evenly.

Sen. Craig Thomas, R-Wyo., said his state gets only $10 million out of $3 billion in annual grants. "Some people think all we have is cows and sheep," he said, stressing that Wyoming also has an important energy base that could be a target.

But Sen. Judd Gregg, R-N.H., who opposes the legislation, said, "The money should go to the threat" -- such as New York City and Washington, D.C., with their subways, commercial landmarks and political centers -- even though that would mean less money for his state.

The House version is more in line with the 9/11 commission's final report, which concluded that "homeland security assistance should be based strictly on an assessment of risks and vulnerabilities," adding, "Congress should not use this money as a pork barrel." The House bill does not specify a dollar amount for federal grants to states or for the emergency communications program.

Both bills would provide the 45,000 airport screeners, whose jobs were federalized when the Homeland Security Department was created after Sept. 11, with collective-bargaining rights, with the rights in the House bill somewhat stronger. That sparked the veto threat from the White House, which said Homeland Security must have no impediments to the flexibility it needs to move workers around in an emergency.

The administration also has voiced objections to House language requiring screening of U.S. cargo in foreign ports or inspection of aircraft cargo, citing expense and practicality concerns.