EDIT: The research I found looks at income inequality, not wealth as the question asks.
Specifically with respect to social welfare spending (not necesserily taxation), the following articles from 2003 seem to suggest the opposite is true.
de Mello and Tiongson:
The political economy literature suggests that redistributive spending is higher in unequal societies due to median voter preferences. Alternatively, it can be argued that unequal societies may spend less on redistribution because of capital market imperfections. Based on different data sources, the cross-country evidence reported in this paper suggests that more unequal societies do spend less on redistribution.
Moene and Wallerstein:
The empirical relationship between inequality and social-insurance spending as a share of GDP in advanced industrial societies differs across policies. For many policies--pensions, health care, family benefits, poverty alleviation--spending is largely uncorrelated with the inequality of wages and salaries. But for a significant set of policies that constitute roughly 30 percent of the welfare benefit--unemployment insurance, active labor-market policies, sickness pay, disability insurance, and occupational illness and injury--spending is significantly more generous in countries with a relatively egalitarian pretax distribution of wages and salaries.
But your question is framed somewhat more broadly. Inequality may potentially lead to greater spending in other areas like healthcare, police, and so on. I'm not seeing any really comprehensive studies that try to take account of all that. In terms of deficits, Larch (2010) finds that "a more unequal distribution of income can weigh on a country's fiscal performance." This does not necessarily show that net taxes are lower in more unequal societies, but Larch does hypothesize that "an increase in the inequality of income tends to soften the relative preference for fiscal discipline". So I would say to answer your broader question, more research may be needed.