This article by Investopidia looks in detail at the tax policies of the Reagan and Clinton administrations and goes over how their tax policies impacted the economy. On one side Reagan's supply side policies which relied on low taxes oversaw large growth in the US economy but before unemployment went down and GDP went up, the inflation rate spike along with interest rates causing a recession for 2 years which perhaps shows the volatility that can arise from an extremely fast cut in taxes. On the other side Clinton's tax raises on the top tax brackets and Corporations saw a smaller but more but less volatile level of growth. Overall this article illustrates the difficulty in measuring the actual effectiveness of changes in taxation on the budget deficit as it can be difficult to tell overall how much change is due to taxation versus deficit spending for example.
This academic journal takes a more qualitative stance on the effect of taxes on the larger economy because the opinion taken in this journal is that raising or lowering taxes is not the most important factor in reducing or increasing a deficit, but rather the writer of this journal believes that more attention should be payed towards if cuts in taxes are replaced with incentives for things such as investment or increased spending which can ensure beyond a reasonable doubt that the decrease in taxes will actually lead up to a difference in the budget deficit.
This article on how taxes impact corporate and individual levels of investment seems to me to be evident of how increasing taxes can worsen a government deficit as investment is a major driving factor in wealth creation and economic growth. Taxes on investment reduce the profit motive on investment which will disincentive investment. Also highlighted in this article is the complex tax laws surrounding investment income, large firms with specialized branches to deal with taxes may be able to find loopholes and increase profit margins but smaller firms and individuals without this luxury may disproportionately feel the burden of investment taxes thus raising the barriers of entry for investment reducing private sector investment.
This article from the Tax Foundation clearly illustrates through the theory of constrained savings how government involvement in the savings and borrowings market (especially through deficit spending) can negatively impact the level of investment in an economy which can ultimately lead to less economic growth and an even larger deficit.