I encourage Yingluck Shinawatra to hang on to her post until Parliament can be convened to elect a new prime minister. Don't yield to the mobs. Don't resign.
You are caretaker PM and there is no Parliament right now. If you resign, who will take your post? There is no law that can be applied under such conditions. If they want you out, let them drag the Army into staging a coup. Or they can conspire with the Constitutional Court to oust you, as they did with premiers Samak Sundaravej and Somchai Wongsawat. Apparently the Army and the court are too full of shame to screw up the country again.
Now the hot potato has fallen into the hand of the Anti-Corruption Commission. Let the agency nit-pick at your record to see if it can scrape up any charges.
In any event, don’t resign. If you do, you betray the 15 million who voted for you. Let them launch a military or judicial coup to oust you, so they show the world how ridiculous and biased are our so-called independent institutions are.