Identifying and managing effectively the Technical Debt has become an issue of great importance over recent years. In cloud marketplaces, where the cloud services can be leased, the difficulty to promptly predict and manage the Technical Debt has a significant impact. In this paper, we examine the Technical Debt, which stems from budget constraints during the software development process as well as the capacity of a cloud service. In this context, the budget and the cloud service selection decisions may introduce Technical Debt. Towards reaching a conclusion, two approaches are taken into consideration. Initially, a cost estimation approach is researched, which is related to implementing Software as a Service (SaaS) in the cloud for three scenarios aiming to predict the incurrence of the Technical Debt in the future. The Constructive Cost Model (COCOMO) is exploited, in order to estimate the implementation cost and define a range of secureness. In addition, a Technical Debt quantification approach is adopted, which is associated with leasing a cloud Software as a Service (SaaS), towards indicating the most appropriate cloud service to be selected.