WASHINGTON—Democrats worked Friday to resolve disagreements over tax increases and expanded healthcare coverage in their roughly $2 trillion social policy and climate framework, with lawmakers studying a potential levy on billionaires to help fund the package.

Top Democrats hope to nail down an outline for the legislation in the coming days, racing to meet an Oct. 31 deadline to vote on a separate, roughly $1 trillion infrastructure bill. Democrats have tied together the House passage of the public-works bill with an agreement on the social policy and climate package, a delicate two-step that has taken months.