The PDP and the APC traded insults on Monday after the opposition accused the ruling party of inciting the violence that erupted on the streets of Kano in the wake of Sanusi's appointment.
How Jonathan responds is still key, with a snub to Sanusi likely to widen the gulf between the PDP and the electorate in the north.
Nigeria's traditional leaders, including the emir, have few constitutional powers but wield great influence as custodians of both religion and tradition.
An unnamed source close to Kwankwaso was quoted as saying by the Leadership newspaper on Monday that the governor's decision was based on the principle of "my enemy's enemy is my friend".
"Where will the president go now in Kano? Will he now come to Kano and bow to a man he suspended from his job for doing the right thing?" the source added.
"And what will happen to all the court cases against him? You can't drag the Emir of Kano to court."
Thomas and Debo Adeniran, from the Coalition Against Corrupt Leaders pressure group, however, said the onus should not all be on Jonathan to build bridges.
Sanusi should also put their differences aside, they said.
The new emir has a responsibility to help tackle the increasingly violent insurgency by Boko Haram militants across Nigeria's north and there was a bigger picture to consider.
"His (Sanusi's) selection should not be politicised because he is now the father of all," said Adeniran.
"It's customary and traditional that the president should pay him homage in Kano as the institution he represents is non-partisan."