Congress isn't the lender. Congress is the borrower. The revenue is set by Congress. The debt limit is set by Congress. The debt is the responsibility of Congress. The lender (people who invest in US bonds) is still willing to lend at very low interest rates. They have nothing to do with this crisis.
This is completely the problem of Congress. No one else is causing the problem.
Obama isn't saying that Congress isn't needed here. In fact he is saying the exact opposite. He is saying "**** your blackmail attempt and DO YOUR ******* JOB!". The President has said repeatedly that Congress created this problem and that Congress needs to fix this problem.
I don't believe that the president should do Congress' job for them. And, I don't think he will.