The military ousted Morsi July 3 after millions of Egyptians took to the streets to demand he step down, accusing him of giving the Brotherhood undue influence and failing to implement vital reforms or bolster the ailing economy.
But Rep. Eliot Engel, D-N.Y., said he supports the president's approach.
"These are very, very difficult choices," said Engel, the top Democrat on the House Foreign Affairs Committee. "I'm very unhappy, obviously, with the crackdown. But we essentially have two choices in Egypt. And that's a military government, which hopefully will transition as quickly as possible to civilian government, or the Muslim Brotherhood. I don't think the Muslim Brotherhood is a choice."
Sen. Jack Reed, D-R.I., said Congress should give the president flexibility in dealing with Egypt.
"I do believe we have to change our aid," said Reed, a senior member of the Senate Armed Services Committee. "I think also we have to have included in the legislation a national security waiver, because we have to give the president not only the responsibility to deal with the government of Egypt but also flexibility."
Sen. Rand Paul, R-Ky., said U.S. aid to Egypt was more likely to "buy a chateau in Paris" for an Egyptian military leader than "bread in Cairo" for the poor.
"I don't think we're buying any friendship with the Egyptian people," Paul said, especially when people see tanks supplied by the U.S. to the Egyptian military on the streets of Cairo.
"We are not winning the hearts and minds of the Egyptian people," said Paul, a member of the Senate Foreign Relations Committee. "The aid has to end."
Sen. Bob Corker, R-Tenn., had resisted calls to cut off aid. But on Sunday, he switched positions.
"I think we need to look at the tiers of our aid," said Corker, top Republican on the Senate Foreign Relations Committee. "Let's face it, most of the aid has gone out the door this year."
Corker said he expects Congress to debate next year's aid this fall, after lawmakers return from their summer recess.
"Look, I condemn what's happened with the military, but I also condemn what in essence was a political coup by the Muslim Brotherhood," Corker said. "And we need to move this debate along and this fall hopefully, again, focus on what is our national interests. And there still are things within Egypt that are very much in our national interest. And we need to keep the lines of communication open."
McCain spoke on CNN's "State of the Union," King and Paul made their comments on "Fox News Sunday," Reed spoke on NBC's "Meet the Press" and Engel, Ellison and Corker appeared on ABC's "This Week."