Briefers including White House national security adviser John Brennan and FBI Director Robert Mueller will guide senators through a simulated cyber attack that damages New York City's electrical grid during a heat wave.
The National Security Agency also will be involved, a staffer said.
"The classified scenario is intended to provide all senators with an appreciation for new legislative authorities that would help the U.S. government prevent and more quickly respond to cyber attacks," said White House spokeswoman Caitlin Hayden.
One bill under consideration - which is backed by Senate Majority Leader Harry Reid and has some Republican support - could require upgrades for critical infrastructure overseen by the Department of Homeland Security.
That bill is aimed at identifying security shortfalls for critical U.S. infrastructure.
Another - backed by Senator John McCain and largely supported by other Republicans - would require federal contractors to inform the government about cyber threats and make it easier for government regulators and corporations to communicate about threats. But it would not affect critical infrastructure.
There has been widespread and growing concern about incursions into U.S. networks by hackers looking to steal everything from state secrets to credit card numbers.
Victims have included defense contractors like Lockheed Martin Corp, Web search leader Google Inc, Citigroup bank and exchange operator Nasdaq OMX.
Politicians have not been immune. In 2008 hackers targeted President Barack Obama's and McCain's presidential campaigns.
But companies have lobbied hard to head off any regulation.
In the U.S. House of Representatives, lawmakers are considering legislation that overlaps with the Senate measures on some points but steers clear of requirements.
In December the House Permanent Select Committee on Intelligence approved a bill that would expand a pilot Pentagon program for sharing classified and sensitive threat information with defense contractors and their Internet service providers.
(Reporting By Diane Bartz; Editing by Xavier Briand)