Veto Threats and Vetoes in the George W. Bush and Obama Administrations [April 30, 2020] [open pdf - 1MB]
From the Summary: "The Framers checked congressional legislative power by providing the President the power to veto legislation and, in turn, checked the President's veto power by providing Congress a means to override that veto. Over time, it has become clear that the presidential veto power, even if not formally exercised, provides the President some degree of influence over the legislative process. Most Presidents have exercised their veto power as a means to influence legislative outcomes. Of 45 Presidents, 37 have exercised their veto power. This report begins with a brief discussion of the ways Presidents communicate their intention to veto, oppose, or support a bill. It then examines the veto power and Congress's role in the veto process. The report then provides analysis of the use of veto threats and vetoes and the passage of legislation during the George W. Bush Administration (2001-2009) and the Obama Administration (2009-2017) with some observations of the potential influence of such actions on legislation."
Congressional Research Service: https://crsreports.congress.gov/