DNA polymerase delta (Pol δ) plays several essential roles in eukaryotic DNA replication and repair. At the replication fork, Pol δ is responsible for the synthesis and processing of the lagging-strand. At replication origins, Pol δ has been proposed to initiate leading-strand synthesis by extending the first Okazaki fragment. Destabilizing mutations in human Pol δ subunits cause replication stress and syndromic immunodeficiency. Analogously, reduced levels of Pol δ in Saccharomyces cerevisiae lead to pervasive genome instability. Here, we analyze how the depletion of Pol δ impacts replication origin firing and lagging-strand synthesis during replication elongation in vivo in S. cerevisiae. By analyzing nascent lagging-strand products, we observe a genome-wide change in both the establishment and progression of replication. S-phase progression is slowed in Pol δ depletion, with both globally reduced origin firing and slower replication progression. We find that no polymerase other than Pol δ is capable of synthesizing a substantial amount of lagging-strand DNA, even when Pol δ is severely limiting. We also characterize the impact of impaired lagging-strand synthesis on genome integrity and find increased ssDNA and DNA damage when Pol δ is limiting; these defects lead to a strict dependence on checkpoint signaling and resection-mediated repair pathways for cellular viability.