A senator who will help determine whether the auto industry gets a $15 billion bailout said Sunday the head of General Motors should step down, telegraphing what could be a congressional demand for a top-line shake-up in Detroit in exchange for financial life support.

Rick Wagoner, the chief executive of GM, “has to move on,” Christopher Dodd (D-Conn.), chairman of the Senate Banking, Housing and Urban Affairs Committee, said on CBS’ “Face the Nation.”

“I think you have got to consider new leadership,” Dodd said. Asked if that should be a condition of any bailout, he said, “I think it is going to have to be part of it.”

“I think it’s clear GM is in the worst shape,” Dodd said.

Senior lawmakers hope next week to present a proposal for votes in both the House of Representatives and the Senate where there has been widespread skepticism about a bailout.

The companies have said they would accept strict terms as conditions for aid. GM and Chrysler said they would go so far as to reconsider a merger if it meant getting federal funds. Congress is not expected to demand such a step this time.

“The last thing I want to see happen is for the auto industry to disappear, but I’m also concerned that we don’t put $10 billion or $20 billion or $30 billion or whatever billion dollars into an industry, and then, six months to a year later, they come back hat in hand and say, ‘Give me more,’ ” Obama said.

Asked whether the top executives should remain in the jobs, he said: “Here’s what I’ll say, that it may not be the same for all the companies. But what I think we have to put an end to is the head-in-the-sand approach to the auto industry that has been prevalent for decades now.”