Effective cell invasion into thick electrospun biomimetic scaffolds is an unsolved problem. One possible strategy to biofabricate tissue constructs of desirable thickness and material properties without the need for cell invasion is to use thin (<2 μm) porous electrospun meshes and self-assembling (capable of tissue fusion) tissue spheroids as building blocks. Pre-stretched electrospun meshes remained taut in cell culture and were able to support tissue spheroids with minimal deformation. We hypothesize that elastic electrospun scaffolds could be used as temporal support templates for rapid self-assembly of cell spheroids into higher order tissue structures, such as engineered vascular tissue. The aim of this study was to investigate how the attachment of tissue spheroids to pre-stretched polyurethane scaffolds may interfere with the tissue fusion process. Tissue spheroids attached, spread, and fused after being placed on pre-stretched polyurethane electrospun matrices and formed tissue constructs. Efforts to eliminate hole defects with fibrogenic tissue growth factor-β resulted in the increased synthesis of collagen and periostin and a dramatic reduction in hole size and number. In control experiments, tissue spheroids fuse on a non-adhesive hydrogel and form continuous tissue constructs without holes. Our data demonstrate that tissue spheroids attached to thin stretched elastic electrospun scaffolds have an interrupted tissue fusion process. The resulting tissue-engineered construct phenotype is a direct outcome of the delicate balance of the competing physical forces operating during the tissue fusion process at the interface of the pre-stretched elastic scaffold and the attached tissue spheroids. We have shown that with appropriate treatments, this process can be modulated, and thus, a thin pre-stretched elastic polyurethane electrospun scaffold could serve as a supporting template for rapid biofabrication of thick tissue-engineered constructs without the need for cell invasion.