In this paper, the SV-TVP-VAR model is used to study the relationships between income inequality, household debt, and consumption growth in the US. This is of great significance for studying whether household debt can become a “substitute” for income and whether it is possible to achieve sustainable growth in consumption under the background of worsening income inequality. According to the research results, the main conclusions are as follows: Firstly, the widening of income inequality would increase consumption in the short term but restrain consumption in the medium and long term, as the relationship between them would turn from positive to negative. Secondly, household debt could improve consumption in the short term but reduce consumption in the medium and long term, with long-term effects being greater than medium-term effects, which means that the long-term negative impact of US household debt on household consumption would be persistent. Lastly, widening income inequality has led to rising household debt over different maturities.