The giddy euphoria that greeted this week's hard-fought agreement to reopen the government is fast giving way to a sober recognition that the deal is very unlikely to usher in a new era of co-operation between Democrats and Republicans.

President Obama tried to prolong the bipartisan high on Thursday by calling on both parties to reach a more permanent agreement on the federal budget and other vexing issues like immigration reform by Christmas, but early indications from key Republicans suggest that making progress on those things will not be easy.

Congressman Raúl Labrador, an Idaho Republican once seen as a bridge to conservatives in the House of Representatives on the question of legalising undocumented migrants, shot down the idea in remarks that revealed just how much bad blood had been caused by the brinkmanship between Obama and Republicans.

"I think what [Obama] has done over the past two and a half weeks – he's trying to destroy the Republican party," Labrador told conservative activists on Wednesday. "I think that anything we do right now with this president on immigration will be with that same goal in mind, which is to destroy the Republican party and not to get good policies."

Republican leaders were only slightly more optimistic about the prospects for a breakthrough in talks over their radically divergent tax and spending priorities. Though House budget committee chairman Paul Ryan finally sat down on Thursday with Patty Murray, his Democratic counterpart in the Senate, to begin long-awaited 'conference' negotiations, Senate minority leader Mitch McConnell sounded a sceptical note, saying the real problem is Obama's unwillingness to accept that he is not in charge of the government's purse strings.

"I wish them well, but with all due respect to all of my congressional colleagues, there is only one Democrat who really counts: the president," said McConnell in an interview. "He's going to be there for three more years. Maybe he'll have an epiphany."

But not all hope is lost, according to Washington political analysts who are busy picking over the wreckage of the Republican shutdown strategy to work out what it means for the balance of power between moderates and conservatives.

On the face of it, the painful decision by House speaker John Boehner to finally overrule his conservative wing and allow a deal to be passed with the help of Democrats could herald more such violations of the so-called Hastert rule – an unofficial doctrine that requires the speaker to block floor votes that are not supported by a majority of his own party.

Ted Alden, an immigration reform expert at the Council on Foreign Relations, says: "Many of the same 87 House Republicans who voted to reopen the government on Wednesday could easily vote for the Senate immigration bill if it was brought to the floor by Boehner."

But part of the reason why Boehner fought so hard over the shutdown was that on the previous occasions when he violated the Hastert Rule to allow for bipartisan votes on high-profile issues like the fiscal cliff, relief spending after hurricane Sandy and legislation to prevent violence against women, he angered his caucus and weakened himself.

Boehner is often simplistically portrayed by Democrats as frightened of risking his members' wrath again, and merely trying to cling on to his job as speaker, suggesting it might be easier for him to stand up to the 30 or 40 hardline Tea Party supporters in the future now that their shutdown strategy has failed.

Yet Wednesday's vote points to an underlying problem for moderate Republicans who choose to strike deals with Democrats – one that won't go away overnight.

The 144 Republicans who voted against the agreement to reopen the government were not all Tea Party activists, but many feared that appearing to side with Democrats could invite a challenge from more conservative rivals during primary elections, especially if they are criticized by activist groups that monitor ideological purity.

"The problem is that tactical decisions have been made into ideological decisions," says Chris Henick, a Republican strategist and former adviser to George W Bush. "Somehow a senator or congressman who otherwise has a 98% rating from interest groups suddenly might face a primary challenge just because they disagreed with the [shutdown] strategy."

For mainstream Republican veterans like Henick, the worry is that political priorities such as promoting economic growth or highlighting the weaknesses of Obamacare have become overshadowed by a desperate battle for survival among congressmen who fear black marks from interest groups will lead to a primary challenge.

But there are signs that this underlying cause of Washington's dysfunction may finally have reached its limits.

While rightwing activist groups such as the Heritage Foundation and Freedom Works may continue to promote conservative candidates at the expense of anyone daring to compromise with the Democrats, major Republican donors and representatives of big business like the chamber of commerce were shocked at how close America came to financial catastrophe during the budget standoff.

"Heritage and Freedom Works will double down but people tell me the chamber [of commerce] has been really chastened by this," says Alden. "I think business will refuse to fund Tea Party candidates now, which will at least even the playing field for moderates."

If House Republicans' fear of losing their jobs before they even get to the general election subsides, longer term electoral interests may encourage the GOP to broaden its base of support through immigration reform and force economic concessions from Obama that will help the party repair its dire standing in opinion polls after the shutdown.

It remains unclear which instinct will prevail, but at least there is a chance the Washington deadlock may begin to ease as a result of the past week's events.

"It's the big existential question right now," concludes Alden. "Does the Republican leadership do things they believe are in the long-term interests of the party and will help them win the White House, or do they act in the short-term interests of House members worried about primary challenges?"