Democrats have criticized Republicans for repeatedly calling for a return to regular order, yet now they are objecting to appointing budget conferees. 

“I don’t think the American people are going to be very sympathetic to hear that Republicans don’t want to appoint conferees because the House would have to take tough votes,” Murray said. “Republicans are now running away from regular order.”

Senate Majority Leader Harry ReidHarry ReidDraft House bill ignites new Yucca Mountain fight Week ahead: House to revive Yucca Mountain fight Warren builds her brand with 2020 down the road MORE (D-Nev.) asked for the unanimous consent agreement, but McConnell again demanded that the conference report not include increasing the debt ceiling or taxes, but Democrats say that would be debating the budget all over again.

“But Republicans know as well as Democrats that is no way to negotiate. Compromise, by definition, should not require unilateral disarmament,” Reid said.

The Senate passed its first budget resolution in years this spring. Murray and her House counterpart, House Budget Committee Chairman Paul RyanPaul RyanOvernight Regulation: Senators call for 'cost-effective' regs | FCC chief unveils plans to roll back net neutrality Overnight Tech: FCC chief unveils plan for net neutrality rollback | Tech on Trump's sweeping tax plan | Cruz looks to boost space industry Not too shabby: Trump tax plan nails corporate rate, errs on income MORE (R-Wis.), have been meeting about setting up a conference, but Democrats say House GOP members are dragging their feet because they’re afraid of a backlash from Tea Party elements within the GOP ranks.

“We want to continue this debate in an open and public way but every time we try Republicans object,” Murray said. “Some Republicans say they want to negotiate a framework behind closed doors before going to conference, but that is exactly what a budget is.”

The House-passed budget cuts $4.6 trillion in spending on top of the $1.2 trillion sequestration cuts already scheduled to take effect, and it balances in 10 years.

Reid said he understands why Republicans don't want to defend their budget in conference.

"It can’t be easy to defend a budget that would end Medicare as we know it. It can’t be easy to stand strong for a plan that asks the middle class to foot the bill for more tax breaks for the rich. ... And it can’t be easy to stick up for the arbitrary, meat-ax cuts of the sequester, which guts the safety net protecting the elderly, the poor, the middle class and our veterans," Reid said. "Or is it possible that Republicans are simply hoping to delay compromise long enough to create another manufactured crisis, as the nation once again approaches a default on its bills?"

The Senate-passed budget has $975 billion in new taxes, does not balance, and turns off sequestration.