After training as a nephrologist, he entered private practice and served in the Puerto Rico National Guard. In 1967, he became politically active, participating in the pro-statehood campaign leading to the July 27 political status plebiscite, as a leader of Estadistas Unidos (Statehooders United), a non-partisan group founded by long-time Statehood Republican Party gubernatorial candidate Luis A. Ferré. On August 20, 1967, at the assembly in Carolina, Puerto Rico at which the organization was dissolved, Padilla and other party leaders proposed the creation of a new political party that would eventually be known as the New Progressive Party (NPP).
In January, 1969, after the NPP's electoral triumph and his own election as a state representative, in spite of being a freshman, he was selected as House Majority Leader for the 1969-1972 term. After the NPP's defeat in 1972 and his own reelection, he served as Minority Whip until 1976. In 1976, after a three-way competition with attorney Baltasar Corrada del Río and Senator Sila Nazario for the NPP nomination for Mayor of San Juan, Padilla was elected to the post, succeeding newly-elected Governor Carlos Romero Barceló and Carlos S. Quirós who served a days-long stint as mayor following Romero's swearing-in as governor and the official beginning of the 1977-1980 term. His term as mayor was marked by a major expansion of sports and community facilities and the first attempt to wrestle with San Juan's looming solid waste crisis. He also served as President of the U.S. Conference of Mayors.
Reelected as mayor in 1980, Padilla became increasingly dissatisfied with Romero and the incumbent governor's capacity to lead the party to another victory in 1984 after barely winning reelection by a less than one-half of one percent margin in 1980. The tensions between both leaders led to Padilla splitting from the NPP and creating the Puerto Rico Renewal Party (PRP), and aspiring for Governor under the PRP banner. Pro-statehood votes in 1984 were split between the PRP and the NPP, which renominated Romero, and the Popular Democratic Party was returned to power through the election to an unprecedented non-consecutive second term of Rafael Hernández Colón as Governor.
After 1984, he returned to medical practice as a nephrologist, serving at the National Capital Area for Kaiser Permanente. In 1991 he was the subject of one television advertisement by Kaiser that was regularly aired across the United States.
Padilla channelled his post-1984 political energies through national initiatives, serving as chairman for the US Council for Puerto Rico Statehood (USCPRS).