PROVIDENCE, R.I. — When her paychecks dried up because of the partial government shutdown, Cheryl Inzunza Blum sought out a side job that has become a popular option in the current economy: She rented out a room on Airbnb. Other government workers are driving for Uber, relying on word-of-mouth and social networks to find handyman work and looking for traditional temp gigs to help pay the bills during the longest shutdown in U.S.