Rep. Gerry Connolly (D-Va.) summed up his feelings in more dire terms: “We are in this horrible purgatory between heaven and hell.” He said “fatalism” had set in: “That there is no way out unless either he or we relent entirely.”

“Democrats are more than willing to try to give him a face-saving way to step down. He doesn’t seem to want to even consider it,” he said.

Some Senate Republicans were also trying to give Trump an off-ramp, including Sens. Lindsey Graham (R-S.C.) and Rob Portman (R-Ohio). They hoped to get as many as 20 Republicans and 20 Democrats to sign their letter to Trump, with the hopes that a substantial Democratic commitment to debating border security and a push from Trump’s own party could shift Washington’s stalemate.

But Republican support for the letter cratered this week amid a widespread belief that the president won’t support opening up the government without a border wall guarantee. The letter still might get sent, according to two people familiar with it. But nobody is super enthused.