After top Democratic aides privately strategized on a novel plan for weeks, the parliamentarian suggested on Monday that the Senate could potentially take an unprecedented step to use a process known as budget reconciliation twice every fiscal year, possibly giving Democrats a chance to move a total of six pieces of legislation with just 51 votes before the end of this Congress, according to officials in both parties and experts of Senate rules. Doing so would effectively circumvent Republicans and a filibuster, which requires 60 votes to overcome, but any package must have a budgetary…