On day 24 of the partial government shutdown, the longest in history, Senate Republicans seemed best placed to negotiate a reopening of shuttered federal departments and threatened services and the restoration of pay to 800,000 workers.

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Lindsey Graham of South Carolina, who has worked assiduously to get close to Donald Trump, said he told the president he should reopen the government temporarily, to pursue a deal. Some Democrats voiced support.

But on Monday morning, en route to New Orleans, where he is due to address a farming convention, Trump told reporters he had rejected Graham’s suggestion.

“I’m not interested,” he said of the senator’s proposal. “I want to get it solved. I don’t want to just delay it. I want to get it solved.”

Trump has remained attuned to conservative media, which speaks for and to his base and on which support has not wavered for his stance on funds for a border wall.

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Earlier in the day, from an understaffed White House, the president suggested via Twitter he had been “waiting all weekend” to negotiate. Trump, who said last month in a meeting with Democrat leaders Nancy Pelosi and Chuck Schumer he would be “proud to shut down the government for border security”, tweeted: “Nancy and Cryin’ Chuck can end the Shutdown in 15 minutes. At this point it has become their, and the Democrats, fault!”

On Sunday night, he had tweeted scattergun blasts of anger. He threatened to “devastate Turkey economically” if it sought advantage from his withdrawal from Syria; he gloated over the personal difficulties of the owner of the Washington Post, Jeff Bezos, whom he called “Jeff Bozo”; and he tweeted what many attacked as a virulently racist message about Elizabeth Warren, the Massachusetts senator running to face him in 2020.

Attaching an Instagram video posted by Warren, Trump wrote that if the senator, “often referred to by me as Pocahontas, did this commercial from Bighorn or Wounded Knee instead of her kitchen, with her husband dressed in full Indian garb, it would have been a smash!”

Contention over Warren’s Native American ancestry, fed with glee by Trump, has dogged her early campaign moves.

Graham strove to pull Trump round to serious politicking, even if his previous attempts to change the president’s mind, such as over Syria, have achieved uncertain success at best. Trump wants wall funding before he signs legislation to open the government. The House speaker, Pelosi, will not pass legislation including Trump’s demand for $5.7bn. Senate Republicans will not pass legislation without it.

Appearing on Fox News Sunday, Graham said: “Before he pulls the plug on the legislative option, and I think we’re almost there, I would urge him to open up the government for a short period of time, like three weeks, before he pulls the plug, see if we can get a deal. If we can’t at the end of three weeks, all bets are off.”

Graham said that if a temporary reopening failed, Trump should use “emergency powers” to bypass Congress, as he has threatened to do, and fund the wall from sources such as military construction budgets, money set aside for disaster relief or asset forfeiture funds taken from criminals by the justice department.

Such a step would attract legal challenges as well as liberal opprobrium, but Democrats could probably not stop it and it could be a political win with Trump’s base. Some advisers say he would have acted to reopen government and exposed congressional inertia – and as a bonus, on becoming tied up in court, would not actually have to build the wall.

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Among congressional Republicans, some fear that such an exercise of executive authority would present a damaging precedent for future White House Democrats. Hopes of a deal involving legal status for Dreamers, undocumented migrants brought to the US as children, linger painfully on.

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If his temporary plan did not happen, Graham said, an emergency declaration would be “the last option, not the first option, but we’re pretty close to that being the only option.”

Trump campaigned on a promise to build the wall, and to have Mexico pay for it. Faced with political reality – in 2017 he told Mexico’s president “we are both in a little bit of a political bind because I have to have Mexico pay for the wall, I have to” – he now says Mexico will do so through savings from a new trade deal. Analysts have undermined that claim.

Congress was due back in Washington on Monday, which dawned under heavy snowfall and with key government functions, from airport security to immigration courts to environmental and food inspections, no closer to being restored. On Friday, workers affected by the shutdown missed their first paycheck of 2019. Stories of hardship, often spreading to those who live with or sell services to such Americans, spread throughout the land.