Two high-stakes games of chicken are playing out on Beacon Hill – one between top Democrats in the House and Senate and the other between Democrats and Republicans in both chambers.

The standoff between the top Democrats is playing out behind closed doors but the policy differences appear fairly clear. Both branches support a $2.8 billion spending bill providing $250 million in additional funding for the state’s overwhelmed emergency shelter system. Senate leaders, however, want to let Gov. Maura Healey decide how best to spend the $250 million. House leaders, by contrast, want to exert more control over how Healey is handling the crisis, directing how the additional money should be spent, including $50 million for overflow shelters to accommodate those on waiting lists for housing.

The two chairs of the House and Senate budget committees initially thought they could privately resolve the differences between the two chambers. When both sides refused to budge, the House and Senate appointed a six-member conference committee to take a shot at compromise, but before that committee could even get started the Legislature adjourned on November 15 for a holiday recess that lasts until January.

The adjournment complicates matters significantly because during the recess the House and Senate generally meet only in informal sessions, where, technically, any member present in the chamber can block action on any piece of legislation.

Pressure to resolve the impasse is intense, coming from both Healey as well as public sector unions. Healey needs the funding in the plan to replenish accounts and close out the fiscal year that ended at the end of June. The public sector unions want the spending plan to win approval so funding for raises their members received in new contracts can be released.

“We need action now,” Healey said Monday on GBH’s Boston Public Radio show. “We need that budget to come through. We’ve got a lot of workers who are counting on that, who we bargained in good faith with and were able to secure raises for the first time in many, many years. So we gotta make good on that. And so, you know, there’s certainly an urgency and I hope, I hope we can get it done this week.”

It won’t be easy. If top Democrats in the House and Senate want to pass the spending plan anytime soon, they need to not only find common ground among themselves but also craft a bill acceptable to every member of the body, including Republicans, who are small in number but suddenly have leverage during informal sessions.

Republicans in the House and Senate have offered a way out of the mess, suggesting the Democratic leaders divide the spending plan into two parts, one part including all of the elements in the spending plan that the two branches agree on and the other the $250 million for the emergency shelter program they haven’t been able to agree on.

“We urge the conference committee to show its support for the state’s workers by immediately reporting out, in part, a bill that funds all pending collective bargaining agreements so it can be moved through both branches and on to Gov. Maura Healey’s desk as soon as possible,”  House Republicans said in a November 20 letter to their Democratic colleagues. “Given the clear support in both branches to fund these items, we are confident there will be no issue with taking up such a bill during informal sessions.”

Senate Republicans released a similar statement, which included a personal appeal from Peter Durant, a state representative from Spencer who recently won a special election for a vacant Senate seat. “Reporting out, in part, these provisions that we can all agree on is both the sensible and responsible thing to do,” Durant said. “The collective bargaining agreements in particular are commitments that we have made to employees; they should not be held hostage to political wrangling.”

The Republican proposal sounds sensible, but Democrats in the House and Senate privately say it’s a trap.They say Republicans want to cut the bill into two parts so they can approve what’s noncontroversial and then block action on emergency shelter funding, which many of them have concerns about.

By keeping all elements of the bill together, Democrats say, their GOP colleagues will be the ones facing pressure if a compromise measure can be crafted. Are the Republicans willing to block raises for public sector unions and deny funding for critical government programs just to score political points about the emergency shelter program?

As these games of chicken play out on Beacon Hill, it’s unclear who will blink. The Republicans have leverage until January, but only if they are willing to use it.