His statement is seen as an attempt to 'climb down' [='back away'] from the strong denial he made yesterday.
a 'climbing plant' [=a plant that attaches itself to something, such as a wall, as it grows up it]
The players 'climbed' into their uniforms [=put on their uniforms] and headed for the field.
(..) - Okay. Good luck, guys. - Hey, wait. Hold up. I don't have any cash. But I do have the pink slip to my car. You just can't climb in the ring with Ali, 'cause you think you box. He knows I can box. Check it out. It's like this. I lose, the winner takes my car. Clean and clear. (..)2001 The Fast and the Furious