A fig leaf (sometimes hyphenated) is something that is used to (figuratively) cover up something that you do not want seen:
something that conceals or camouflages, usually inadequately or dishonestly
So the second sentence would be
The president used the workers as a fig leaf to win over public support.
This is an allusion to the book of Genesis, in which Adam and Eve cover their nakedness with literal leaves from fig trees. It has come to connote a transparent attempt to distract from one's true motivations, e.g.:
“Is Russia really committed to a peace process or is it using the peace process as a fig leaf to try to deliver some kind of military victory for Assad that creates an Alawite mini state in the northwest of Syria?” Hammond told reporters in Rome.
"Britain says Russia trying to carve out mini-state for Assad in Syria", Reuters, 2016-02-02
The austerity agenda has been seized by the Tories as the fig leaf behind which to progressively underfund health and social care, creating today’s crisis.
"Jeremy Hunt is still clinging to his job because he has big plans for April", New Statesman, 2019-02-04