WASHINGTON—Senate Democratic leaders, seeking to break an impasse over Republican-backed spending cuts, on Tuesday proposed broadening the scope of budget negotiations into more politically volatile terrain that includes taxes, subsidies and entitlement programs.

Senate Majority Leader Harry Reid (D., Nev.) said that efforts to bridge the parties' $50 billion difference in proposed budget cuts for the remainder of fiscal-year 2011 could reach beyond domestic discretionary spending and move into tax policy and programs such...