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WASHINGTON — On Day One of the government shutdown, House Chaplain Patrick Conroy opened the chamber's session with a plea for compassion.

"This is a painful day for many across our land," the Jesuit priest said. "May those who possess power here in the Capitol be mindful of those they represent who possess little or no power and whose lives are made even more difficult by a failure to work out serious differences."

"Amen!" Rep. Janice Hahn, a California Democrat, shouted from the front row.

But Conroy's prayer was not to be answered Tuesday, as lawmakers on both sides of the Capitol did little other than trade blame and invective. Mindfulness was not in evidence.

Even as he prayed on the House floor, the priest was interrupted by a musical cellphone ring from the pocket of Rep. Frank Wolf, R-Va. Already, Rep. Michele Bachmann, R-Minn., had injected racially charged imagery into the standoff, telling a far-right website that "President Obama can't wait to get Americans addicted to the crack cocaine of dependency on more government health care."

On the Senate floor Minority Leader Mitch McConnell scornfully said that Democrats would blame the shutdown on "the mean ol' Republicans or the tea party or Fox News or maybe even George W. Bush."

Replied Majority Leader Harry Reid: "My friend, the Republican leader, spoke as if George Orwell wrote his speech."

But God works in mysterious ways. For, in the stalemate that froze the Capitol on Tuesday, there were also the makings of a hopeful dynamic.

Republicans devoted much of the day to protesting that Democrats "won't even sit down and have a discussion" (House Speaker John Boehner) and "literally just voted against working out a compromise " (McConnell). They were absolutely right: Democrats weren't making the slightest effort to compromise. And if Democrats continue not to budge, everybody — even conservative Republicans — will someday be grateful.

Democrats did offer to keep the government running for the next six weeks at current spending levels, which is a minor concession. But their refusal to consider any deal with Republicans that involves weakening Obamacare is good news, because doing so would make the already intolerable situation in Washington worse.

Compromise is usually a happy notion, but in this instance it would invite more chaos. If Democrats agree to weaken health care reform, they will have proved that all it takes to change an existing law is for a minority of lawmakers in one chamber to threaten a rebellion against their own party's leadership.

Under that standard, a small band of future Democrats could shut down the government if a future Republican president didn't agree to, say, strict gun controls, abortion on demand, a carbon tax, a higher minimum wage, expanded Social Security and Medicare benefits or open borders. If Republicans succeed in rolling back Obamacare, they will undoubtedly turn to other items they have already demanded as their price for keeping the government running: restrictions on birth-control access, narrower Medicare eligibility, obstacles to malpractice lawsuits, lighter environmental regulations and more oil drilling.

Had this been the standard before, Democrats might have shut down the government to try to force George W. Bush to end the Iraq war, or to make Ronald Reagan end his arms race with the Soviets.

Maybe that can provide some consolation to Republicans, who are slowly edging toward the realization that they are not going to win this fight. Rep. Charlie Dent of Pennsylvania, one of the few moderates in the Republican caucus, said it was a matter of time before his colleagues accepted the Democrats' offer to keep the government open at current levels.

"We're going to get there," Dent told reporters Tuesday. "More members are arriving at that position. ... There are plenty of us prepared to vote for it."

But first, his Republican colleagues will have to exhaust their complaints about Democrats' refusal to negotiate.

In a House GOP strategy session Tuesday, lawmakers continued to grasp for a winning message; they proposed a few symbolic pieces of legislation to keep the Department of Veterans Affairs, the national parks and the District of Columbia running (all three later died on the House floor). But as they emerged, the message was unchanged: Democrats won't compromise.

"Our goal is to get the Senate to engage," said Rep. Jack Kingston of Georgia.

Protested Rep. Louie Gohmert of Texas: "They won't even have a negotiation."

Nor should they. In this case, compromise will hurt everybody — even, eventually, the Republicans.

Follow Dana Milbank on Twitter, @Milbank.