The hashtag #ارحل, which means simply "Leave," is base on a promise that Abbas made years ago that he would resign if there were even small protests calling for him to leave.
The protests were sparked by the apparent murder of Abbas critic Nizar Banat last month by Palestinian police.
Some of the current criticisms of Abbas now are more centered on his being way too moderate and conciliatory towards Israel, saying that he has no right to accept a two state solution.
This one quotes him as saying that "East Jerusalem is ours and West Jerusalem is theirs," asking what gives him the right to give up 80% of Jerusalem?
This graphic lists the high Palestinian officials who have gone to Israeli hospitals when they are ill, leaving their people to use sub-par Palestinian hospitals. (The Palestinian Authority used to pay for all citizens who needed treatment in Israeli hospitals and stopped that a few years ago.)
The blast at the Al Zawiya market has spawned calls for investigations on why Hamas allows - and encourages - placing military equipment in the middle of civilian areas, knowing that Israel is reluctant to bomb those targets but putting Gaza lives at risk.
Also, last week Hamas forces shot at a car that they claimed sped through a checkpoint. (Yes, there are checkpoints inside Gaza, under full Hamas control.) One of the passengers died and Hamas' story was not consistent with the autopsy results.
Both Hamas and Abbas are trying to distract the criticisms by redirecting anger towards Israel, their usual go-to move. Hamas has resumed allowing incendiary balloons to start fires in Israel and PA prime minister Shtayyeh has been working to get new UN Security Council condemnations of Israel as well as to re-start the moribund Quartet, with a friendlier White House less likely to object.