Tim Burgess is not a fan of a new proposed business tax.

Seattle Mayor Tim Burgess said Tuesday a so-called head tax on employees is "ill advised."

It comes as Council Budget Chair Lisa Herbold unveiled her initial balancing package in council chambers, which included the tax on businesses with gross income over $5 million a year. The bill would establish a tax of $100 per FTE or full-time equivalent. An FTE is a full-time employee or two or more part-time workers with hours that equal 40 per week.

Proponents say the tax would help pay for new shelters, vehicle safe zones, and investments in new rent and income restricted housing units.

Herbold is the fourth councilmember to publicly back the tax, along with Mike O'Brien, Kshama Sawant, and Kirsten Harris-Talley. Four other councilmembers, Lorena Gonzalez, Debora Juarez, Rob Johnson, and Sally Bagshaw, oppose the current proposal. Only Council President Bruce Harrell has not tipped his hand.

Burgess says his budget already includes $63 million in homeless funding, and that's a "62 percent increase since 2014." He says an alternative approach to the tax would be to move forward with an ordinance and tax on short term rentals, like ones operated by Airbnb and Expedia.

The mayor would not say whether he would veto the measure if it made it to his desk.

"I'm not sure," he said. "I'll cross that bridge if I have to."