It could be argued that the power of lame duck presidents cuts both ways since they can act with less fear of reprisal. You may still be right about prioritizing congress.
Related, I once read an AMA on Reddit where a congressional staffer advised everyone to do their best to get op-ed pieces in newspapers which mention your elected officials, since it was their job and the job of the staffers they knew to compile such pieces for review every morning by the legislator.