Model, actress and radio personality Pearl Thusi was in a car accident that left her and her daughte.
Sangomas pay an annual 10 emalangeni ($1.15) license fee, but MP Majahodvwa Khumalo said they had jacked up their fees fourfold in the last few years and should pay more.
"A majority of our people consult traditional healers but the money they pay to government falls far too short of the money they make," he told parliament.
Swaziland's budget deficit ballooned to 15 percent of its annual economic output in 2010 but the government managed to keep itself afloat by running through central bank reserves and delaying payment of wages to civil servants.
The International Monetary Fund (IMF) declined to launch a bailout because of reluctance by King Mswati III, who has at least a dozen wives and a personal fortune estimated at $200 million, to cut royal or military spending.
The IMF has continued to press for reductions to what is officially Africa's most bloated bureaucracy. In an in-depth assessment of the economy published in February, it rated the scope for raising more taxes as "small".