The overarching goal of limiting the increase in global temperature to ≤ 2.0˚ C likely requires both decarbonization and defossilization efforts. Direct air capture (DAC) and CO2 electrolysis stand out as promising technologies for capturing and utilizing atmospheric CO2. In this effort, we explore the details of designing and operating an integrated DAC-electrolysis process by examining some key parameters for economic feasibility. We evaluate the gross profit and net income to find the most appropriate capacity factor, average electricity price, syngas sale price, and CO2 taxes. Additionally, we study an optimistic scenario of CO2 electrolysis and perform a sensitivity analysis of the CO2 capture price to elucidate the impact of design decisions on the economic feasibility. Our findings underscore the necessity of design improvements of the CO2 electrolysis and DAC processes to achieve reasonable capacity factor and average electricity price limits. Notably, CO2 taxes and tax credits in the order of $400 per t-CO2 or greater are essential for the economic viability of the optimistic DAC-electrolysis route, especially at competitive syngas sale prices. This study serves as a foundation for further work on designing appropriate power system models that integrate well with the presented air-to-syngas route.