Things to do....

There is a lot of things to do.

Reflecting his party’s chastened state heading into the next phase, Senator Mitch McConnell of Kentucky, the Republican leader, told the conservative National Review on Thursday, “A government shutdown is off the table.”

Even so, Republicans enter these new talks with one advantage: if the negotiations fail, the next round of across-the-board spending cuts known as sequestration will hit automatically, even deeper than the first. Democrats want to avoid that far more than Republicans do.

Both Mr. Ryan and Ms. Murray struck positive notes.

“Our goal is to do good for the American people, to get our debt under control, to do smart deficit reduction, and to do things we think can grow the economy and get people back to work,” Mr. Ryan said.

Ms. Murray said, “We believe there is common ground.”

By definition, common ground suggests no grand bargain, which would require a much more difficult trade-off where they fundamentally differ — higher tax revenues that Republicans oppose, in exchange for reductions in Medicare, Medicaid and Social Security that Democrats vow they will not entertain without curbs on tax breaks for wealthy individuals and corporations.

With the last-minute settlement, Washington found itself battered, exhausted and about where it was back in March in terms of budget progress. That month, Congressional Republicans and the White House failed to prevent the sequestration cuts from taking effect across military and domestic programs.

The Republican-led House and Democratic-controlled Senate passed vastly different budgets, but Republicans blocked Democrats’ repeated efforts to convene a conference committee to reconcile the differences — until this week.

Congress not only reopened the government through Jan. 15 and raised the nation’s borrowing limit effective to Feb. 7 on Wednesday. It also mandated the formal budget negotiations in a separate parliamentary motion.

“Nobody can guarantee success, but what we can say is that if we don’t make the effort and get together and talk, that would guarantee failure,” said Representative Chris Van Hollen of Maryland, House Democrats’ chief negotiator.

To improve the prospects for some success, the negotiators largely agreed at a closed-door breakfast on Thursday that a deal involving significant new tax revenues and large-scale changes to Medicare, Medicaid and Social Security, whose growth in an aging population is driving long-term projections of growing debt, is not going to happen.

Instead, they agreed, the talks will aim at a more modest, confidence-building measure to replace the sequestration cuts in 2014. Negotiators could aim higher, for a deal saving at least $1 trillion over the next nine years to substitute completely for the arbitrary sequestration cuts. But neither side was hopeful of that.

Even with lower sights, negotiators face the same hurdle over taxes that has ended a series of bipartisan talks in 2011 — between Mr. Obama and Speaker John A. Boehner; between Vice President Joseph R. Biden Jr. and Representative Eric Cantor, the