Sugar-sweetened beverage (SSB) taxes are present in many countries with evidence that they are effective in decreasing purchases of SSBs. However, in Australia where SSB consumption per capita is high, and calls for an SSB tax are frequent, there is no SSB tax and policymakers have stated their lack of support for such a tax. We examined whether political party voting preference and sociodemographic factors affect individuals’ support for an SSB tax, and whether message framing affects this support. A nationally representative sample of 1519 Australian adults was recruited for an online experimental survey. Three persuasive frames and one control frame were randomly provided to participants and measures of agreement towards an SSB tax were assessed. Sociodemographic factors and political party preference were also captured. Message framing had minimal effect on the level of support for the tax. However, participants who received the ‘supportive of food and drink companies frame’ showed the highest positive feelings towards the tax, and participants in rural areas had higher levels of support for an SSB tax when receiving the ‘protecting teenagers’ frame. Participants who voted for conservative (right-leaning) parties and for Labour (a centre-left party) had similar levels of support towards the tax, which was considerably lower than Greens voters. Undecided voters had the lowest levels of support for the tax, and the frames had limited impact on them. These findings highlight the potential role of message framing in shaping public support for an SSB tax in Australia, particularly in the context of voting preference and sociodemographic factors.