WASHINGTON—Democrats, working to unite around a far-reaching social policy and climate bill, are weighing two different approaches to reduce its overall cost: eliminating proposed programs entirely or cutting their duration.

Democrats’ debate over the two options took on fresh urgency this weekend after President Biden said Friday that they would have to shrink the size of the legislation, projected to spend $3.5 trillion over a decade to expand and create education, healthcare, climate and other programs.