WASHINGTON — Sequestration represents a kind of excellence in failure. Lawmakers in Washington couldn’t even design a sword of Damocles correctly. This is depressing, and suggests even the most basic tasks are beyond the reach of our lawmakers. As a result, a lot of people appear particularly glum, as if they gave up optimism for Lent. But what if you decided to embrace hope during the Easter season? Is there any evidence that there could be a rebirth of common sense and progress?

Such a pursuit would require a degree of faith, a reliance on things unseen and a belief in hope over experience. But there have also been some more concrete developments that might at least distract you from greater despair and doubt.

The first is purely procedural. This month, the president, House, and Senate will all present budgets as a part of the standard budget process. Washington getting back to its regular rhythm is no small thing. It represents a return to the central issues of the budget — taxes, spending, and investment — and distance from the blame game of sequestration politics. For Senate Democrats, who have shirked the formality of producing a budget for some time, this alone might seem miraculous.

A return to normal business means there will be hearings and public debates about entitlements and closing loopholes. That might remove some suspicion from the process. The series of last-minute crisis bargaining — the holy trinity of the debt ceiling, fiscal cliff, and sequestration — make people feel like they’re being taken. Yes, any grand bargain will be worked out in a small room too, but if the issues have been aired in a formal way that might raise trust in an ultimate deal. (Warning: business-as-usual also means lobbyists and 100 interest groups will pick apart 100 different elements of any deal. Still this is progress: In a time of total dysfunction, regular dysfunction is preferable.)

Once the larger debate starts, the threshold questions for progress will be familiar: Will Republicans move off their no-taxes posture and will President Barack Obama agree to changes in entitlement programs? Both are possible: Obama has endorsed entitlement changes in public and private — from raising the Medicare retirement age, to means testing it, to changing the formula for Social Security increases. Republicans agreed to $600 billion in revenue. The trick is really binding those two positions in the same deal.

Republicans were absolute in their opposition to replacing the sequestration cuts with tax revenue. That could be a sign of their unwavering resistance to the idea. But it might also have been the macho Republicans were required to show to build trust for a future accommodation.

GOP leaders probably needed to be a little extra macho on sequestration. Many influential Republicans believe that GOP lawmakers conceded to the president in the fiscal cliff and debt limit negotiations. In conversations with GOP aides, it was clear that their bosses believed the base wouldn’t tolerate another perceived surrender. Now at least the party’s leaders can refute the claim that they back down whenever Obama tries to pressure them. If there is ever going to be a grand bargain, GOP leaders will need to sell it to their rank-and-file. If nothing else, Republican leaders can make the pitch now without being shouted down.

We interrupt this story with a bulletin from reality. “We’re done on revenue,” says one GOP aide about any future deal that would include tax revenue. So whatever imagined new trust there may be among the Republican rank-and-file and their leadership is irrelevant because leaders aren’t going to try to sell a deal that includes tax revenue.

Pessimists have a strong case, to be sure. Republicans held out for 22 years before they voted for a tax increase two months ago, and it’s a good bet they don’t want to do that again anytime soon. But the same GOP aides now saying that Republicans are “done on revenue” once said the GOP-controlled House would never vote for a tax increase. In the end, that prediction was wrong. House Speaker John Boehner also said he wouldn’t agree to any debt limit increase that didn’t include an equal amount of spending reductions. That didn’t come to be either.

Furthermore, the GOP’s position isn’t really “we’re done on revenue” — it’s more like “we’re done, unless the president convinces us not to be.” If the president shows willingness to give in on entitlements, enough Republicans might accept some tax increases.

There is at least rhetorical openness among some Republicans to that kind of a deal. On Face the Nation, Sen. Lindsey Graham endorsed a deal where revenue gained through tax reform would go toward deficit reduction in exchange for trimming entitlements. Former Gov. Jeb Bush has said an ultimate deal could include tax revenue.

The benefit of a grand bargain has always been clear to both sides. While a bigger deal means more complexity and lobbyists, it also means more ways to buy off various opponents. Some Republicans can be convinced that voting for revenue that comes from changes in the tax code is OK because those changes will make tax regulations simpler, which will in turn promote growth. Some Democrats can be persuaded that you can only save entitlements by reforming them.

For many Democrats, talk of a grand bargain is another head-fake. Some Republicans may say they are open to a deal, but when the details are put forward, they’ll only ask for more. That is what torpedoed negotiations in the summer of 2011 and every attempt since. One reason the rhetoric never matches up is that politicians can have it both ways. They can proclaim the desire for a compromise approach, but then raise the bar on specific measures well beyond any reasonable standard. A cynic might also point out that Graham, who faces a possible primary challenge, is going to have a lot of incentives to set a standard for entitlement reform that Obama can never meet.

If you insist on being an optimist, you must believe that elections and polls mean something, but that the sequestration fight wasn’t a fair test of that proposition. Polls show there is overwhelming public support for a budget agreement that includes revenue from tax increases and spending cuts. In a recent Pew poll, 76 percent of people said that the president and Congress should focus on a combination of spending cuts and tax increases to reduce the budget deficit. Just 19 percent agree with the Republican position that tax increases should be kept out of a deal.

Despite a core group of Republicans who will never vote for revenue from tax increases and a smaller group of Democrats who won’t vote for entitlement reform, there are enough politicians who will feel enough pressure to back a deal. The fiscal cliff, debt limit, and sequester negotiations took place in an environment cluttered by claims and counter-claims about the disasters that would result. In a more extended, slightly longer debate, the ultimate choices may be clearer and less likely to be sabotaged by histrionics. Lawmakers and the press will have less cause to get distracted.

Math may finally kick in, too. If lawmakers want to tackle the deficit, after sequestration cuts, there’s just not that much more you can cut out of the discretionary part of the budget to solve the problem and stay in office. You can only get deficit reduction of a significant size from the tax code or entitlements, and in a divided government that means deal making.

A final grand bargain only happens if the president can build what he calls the “common sense caucus” in the Senate. He was on the phone with Republicans over the weekend trying to start the negotiations. The White House thinks there are enough Republican senators open to reason.

The president’s pitch is that while the sequester does nothing to reform entitlements, nothing to reform the tax code, and ultimately does little to reduce the deficit, the big deal the president wants cuts spending, finally takes on entitlements (though not fully), and all for the price of revenues that Boehner has put forward before. On the Democratic side, there are several senators up for re-election in conservative states who need to show that they are cutting spending and reducing the deficit.

A bipartisan group of senators might give Boehner cover to allow the House to take a vote and not require that it pass with a majority of Republicans. He’s already taken that route three times since the election — on the fiscal cliff deal, Hurricane Sandy relief, and the Violence Against Women Act.

Maybe this case proves the difficulty of being an optimist in Washington today better than the underlying reasons for optimism. Retaining faith requires some breath holding, self-delusion and, in the end, prayer.

Dickerson is Slate’s chief political correspondent and author of “On Her Trail.” He can be reached at slatepolitics@gmail.com.