Elon Musk said Saturday he'd be willing to pay the salaries of TSA agents during the Homeland Security shutdown, as President Trump suggested the possibility of using ICE agents to keep airports moving instead.Why it matters: The shutdown is causing chaos for travelers and gridlock in Congress, with few solutions on the horizon. Pressure to resolve the shutdown is intensifying as airport delays worsen and staffing risks escalate.Driving the news: "I would like to offer to pay the salaries of TSA personnel during this funding impasse that is negatively affecting the lives of so many Americans at airports throughout the country," Musk posted to X early Saturday morning.About five hours later, President Trump posted to Truth Social that if Democrats didn't agree to a funding deal, he would deploy ICE agents to airports, "where they will do Security like no one has ever seen before."Between the lines: It's not clear what prompted Musk's abrupt offer a month into the shutdown, or how either solution would work.Based on TSA's headcount, Musk paying officer salaries could run more than $40 million a week, a rounding error for the world's richest person. Substituting TSA agents with ICE could have its own complications, including a lack of training on screening equipment.For the record: The White House did not immediately respond to a request for comment on Musk's offer. What to watch: Democrats have recently pivoted to new tactics in an attempt to end the impasse, though there are few signs of movement.The bottom line: TSA screens more than 2.5 million passengers a day.They likely don't care who's doing the screening, or who's paying the screeners, as long as they can stop waiting in line.