Grass-covered bread for congress? (4,2,3,3)

'congress?' is the definition.
(roll in the hay is a kind of congress)

'grass-covered bread' is the wordplay.
I cannot really see how this works, but
'grass' could be 'hay' (hay is dried grass) and 'hay' is present in the answer.
'covered' could be 'in' (I've seen this in other clues) and 'in' is found within the answer.
'bread' could be 'roll' (roll is a kind of bread) and 'roll' is found within the answer.
The remaining letters 'the' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'for' acts as a link.

Can you help me to learn more?