That committee held a hearing on the Kingston spill.
Boxer said Congress could use "the power of the purse" to transform TVA into "a model" for green power research, development and use.
Cleaning up the Kingston spill, which dumped 5.4 billion cubic yards of fly ash over 300 acres and into the Emory River, will cost millions of dollars, and TVA hasn't publicly given an estimate.
"That's a cost of (using) coal we really haven't looked at," Boxer said.
Though a federal agency, TVA is funded entirely by its operations and no longer receives money from the federal budget. A Boxer staffer could not say after the briefing whether Boxer meant to restore federal appropriations, at least for green power technology programs, or intended to investigate some other funding mechanism.
Republican members of the committee, including U.S. Sen. Lamar Alexander of Tennessee, attended a GOP planning retreat for the new session of Congress and weren't present at the briefing. Alexander was the host of the retreat.
Meanwhile, the chairman of the committee's counterpart in the House of Representatives said he supports federal oversight of coal ash ponds. The U.S. Environmental Protection Agency doesn't consider fly ash to be a hazardous waste, and a New York Times article published Wednesday reported there are 1,300 similar facilities across the country, many unregulated by state governments. In Tennessee, fly ash facilities are regulated as Class II landfills by the state Department of Environment and Conservation.
U.S. Rep. Nick Rahall, D-W.Va., chairman of the House Natural Resources Committee, said fly ash, which is coal combustion waste, should be treated similarly to coal slurry, which is a byproduct of coal mining.
"Coal ash impoundments like the one that broke last (month) in Tennessee ought to be subject to some federal regulations to ensure a basic level of safety for our communities," Rahall said in a statement.
TVA President and CEO Tom Kilgore is scheduled to testify before the Senate committee along with Roane County Emergency Management and Homeland Security Director Howie Rose and Stephen Smith, a longtime agency critic and executive director of the Southern Alliance for Clean Energy.