IF THE country’s recent unhappy experience with threatened defaults and fiscal deadlines has taught us anything, it is that compromise happens when the Senate — and especially the Republican side of the chamber — steps up. The Republican majority in the House is simply too far to the right of the Obama White House, and too divided internally, to strike a deal. By contrast, the GOP members of the Senate — not a majority, but armed with the leverage of the filibuster — may still be moderate enough, and united enough, to bargain effectively.

At least that’s how the 2011 debt-ceiling showdown and the 2012 “fiscal cliff” dispute got resolved. Each time, sterile confrontation between the House and the White House gave way to talks between Democrats and Senate Minority Leader Mitch McConnell (R-Ky.). Those talks produced a lowest-common-denominator bargain that left long-term fiscal problems mostly unaddressed — but the legislation managed to pass both houses on a bipartisan basis and keep the country afloat.

In the current crisis, however, Senate GOP ultras, led by Sen. Ted Cruz (R-Tex.), have occupied center stage, and Mr. McConnell was sidelined by the threat of a primary challenge from a Cruz clone in his 2014 reelection race.

So it is positive indeed that Senate Republicans, headed by moderate Susan Collins of Maine, are back in business and developing a legislative vehicle, quietly supported by Mr. McConnell, that would both end the shutdown and extend the government’s borrowing authority — and it is even more promising that they spent two hours talking about it with President Obama on Friday.

This hardly makes Mr. McConnell, or anyone else in his caucus, a hero. To the contrary, he and his fellow GOP leaders could have saved the country (and themselves, by the way) a lot of heartburn if they had stood up to Mr. Cruz much more forthrightly much sooner. Nor are the current dealings between the GOP senators and Mr. Obama any likelier to produce the much-needed “grand bargain” — to include both higher revenue and lower Medicare and Social Security outlays — that eluded negotiators in 2011 and 2012.

However, details of Ms. Collins’s package released so far suggest that it has advantages — raising the debt ceiling unconditionally and for about twice as long as House Republicans contemplate; a bill to reopen the government and fund it at current levels for up to a year, but with more agency flexibility to allocate budget dollars. It also makes trade-offs we’d rather not see: no definitive end to the sequester and a reduction or delay of the medical-device tax, which helps defray the cost of Obamacare, paid for with a gimmicky change to corporate deductions for pension contributions.

Ms. Collins’s bill would give Congress more time to work on entitlement reform before the next debt ceiling hits, but we’d like to see it incorporate Rep. Paul Ryan’s notion of explicitly linking an end to sequester spending caps with reductions in entitlement spending. This was probably the most positive idea to emerge from what was otherwise near-total confusion in the House.

Nevertheless, there is still plenty of time and space for these approaches to converge and to win acquiescence from a sufficient number of Democrats and Republicans. Friday’s events suggest that, at last, all the players — the House, the Senate and Mr. Obama — are, if not in agreement, at least in the game.