If both the Republicans and the Democrats present budgets in Congress, the Republicans tend to loose popular support. Republican "no new taxes all cuts" budgets spook people. The Ryan Budget, for instance was what a Republican budget is about. Things like the huge cuts in Medicare and Medicaid spooked the public. After the Ryan budget was presented, it was said that Democrats gained a seat in Congress that normally votes Republican. That seat from a district in New York State happened to be up for election soon after the Ryan Budget was unveiled.
Democratic plans for balancing milder budget cuts with tax increases on the wealthy seem more popular when the dust settles and the actual figures are presented.