The bipartisan infrastructure bill is a win for Biden. Now comes the hard part.

After months of negotiations and several points when talks were on life support, the Senate voted 69-30 to pass a bipartisan infrastructure bill.

That was supposed to be the hard part. But Senate Minority Leader Mitch McConnell, R-Ky., didn't just hold off on filibustering one of President Joe Biden's top priorities — he voted for it himself. Nineteen Republicans voted in favor of the final package, which will invest billions in roads, public transit, bridges, water systems and expanded broadband internet access.

Now the bill heads to the House — where it runs headfirst into a challenge that Speaker Nancy Pelosi, D-Calif., will have to unravel in the next month.

Personally, I love puzzles. That's not a metaphor — I mean that literally. Not so much jigsaws or that one peg game they have in Cracker Barrels. But word puzzles absolutely delight me. So does untangling knots. A clump of jewelry that's merged into a metal ball of necklaces and chains, the string of lights that were haphazardly shoved into a box after Christmas, the bundle of cords that every millennial keeps in a drawer despite having no idea what they belong to anymore? I love them all.

There's something inherently satisfying about the feeling of sinking your fingers into the chaos and feeling how it all fits together, determining what needs to go slack so another thread can be wriggled loose. It's a process than can swing from deeply Zen to utterly frustrating and back in a heartbeat as you discover what needs to loop back over itself to finally be set free.

I don't envy the job ahead for Speaker Nancy Pelosi and Senate Majority Leader Chuck Schumer.

But to shift back to the metaphorical, I don't envy the job ahead for Pelosi and Senate Majority Leader Chuck Schumer, D-N.Y. Immediately after passing the bipartisan bill, Senate Democrats voted to begin consideration of the next step in Schumer's two-track infrastructure plan — a $3.5 trillion budget resolution.

That massive package is the one that includes most of the progressive items in Biden's American Jobs Plan and American Families Plan — things like investing in universal pre-kindergarten, mitigating climate change and taxing the wealthy and corporations to pay their fair share. It's a bill that will need only 50 votes (plus the vice president as a tiebreaker) to pass the Senate once it is completed, which means two things: First, that Republicans hate it on principle — but can't stop it themselves. Second, that Democrats have zero room for error.

The latter point is where the puzzle comes in. Because there are potential spoilers in both the House and the Senate. On one hand, you have Sen. Kyrsten Sinema, D-Ariz., one of the lead authors of the bipartisan bill. In a statement to The Arizona Republic last month, Sinema hinted that she might not wind up supporting the full $3.5 trillion framework that Schumer and Senate Budget Committee Chair Bernie Sanders, I-Vt., had put forward:

Sinema, D-Ariz., told The Arizona Republic on Wednesday she had reviewed the Senate Budget Committee’s spending framework and has told Senate leadership and Biden that she supports many of its goals, including job growth and American competitiveness.

“I have also made clear that while I will support beginning this process, I do not support a bill that costs $3.5 trillion — and in the coming months, I will work in good faith to develop this legislation with my colleagues and the administration to strengthen Arizona’s economy and help Arizona’s everyday families get ahead,” Sinema said in a written statement.

Democrats will need every vote to pass this package, and Sinema knows that. In kvetching about the final price tag, she's positioning herself as a dealmaker who can trumpet that she helped keep spending in Washington from running out of control. Of course, we have no idea what amount would make sense to her — $2.9 trillion? $3.49 trillion? — or what programs she'd want to see get less money or be cut altogether, which gives the whole thing an air of arbitrary capriciousness.

But the more immediate issue is in the House, for once. Pelosi said in June that she would not bring the bipartisan bill to the floor until she also has the broader infrastructure package in hand for her members to vote on. She even reaffirmed that view at her weekly news conference Friday.

That's drawn the ire of some of her more moderate members, several of whom circulated a letter last week calling the speaker's strategy into question. "As soon as the Senate completes its work, we must bring this bipartisan infrastructure bill to the House floor for a standalone vote," reads the draft letter, obtained by CNN. "This once-in-a-century investment deserves its own consideration, without regard to other legislation."

In response, progressives shot the speaker a letter of their own Tuesday. If a vote on the bipartisan infrastructure measure is held before the Senate "has passed budget reconciliation legislation deemed acceptable" by the Congressional Progressive Caucus, it's going to be a "no" from its 96-member strong crew, the letter cautioned. Given that Pelosi can afford to lose only three of her members and still pass a bill with no GOP support, it seems on the surface that Pelosi is in a bind.

For a minute there, I thought that Pelosi might be looking to pull an Alexander the Great on this particular Gordian knot. You see, the House is in the middle of its August recess. The Senate would be, too, if Schumer hadn't put off vacation to get the bipartisan bill and the budget resolution over the line.

That budget resolution is just part one of the process, though, in that it provides guidelines about how much money is going to be spent, the details of which various committees are then instructed to go figure out. The deadline Schumer has set for that work to be finished is Sept. 15, after which the results are smushed together into a final reconciliation bill.

What Pelosi knows, and NBC News deputy Washington editor Ginger Gibson filled me in on, is that the same process has to happen in the House. It's a much quicker two-step on that side of the Capitol, but it still takes time to finish. Sticking with the schedule posted on the House legislative calendar would have meant the soonest that work could begin is Aug. 31.

Even if Pelosi does get the votes for the first resolution, that doesn't make the final reconciliation bill a foregone conclusion

But on Tuesday evening, House Majority Leader Steny Hoyer, D-Md., sent a message informing his members of a change of plans: "For your scheduling purposes, assuming that the Senate does, in fact, complete work on a budget resolution, the House will return to session on the evening of August 23 to consider that budget resolution and will remain in session until our business for the week is concluded."

Notably, there's still no mention of voting on the bipartisan infrastructure bill in Hoyer's message — but it does leave the possibility open. Now, Pelosi is one of the best vote counters the House has seen, so I doubt she'd pull everyone back if she didn't have things locked up for the budget resolution. But I'm honestly not sure what she has planned to appease both wings of her caucus.

Even if Pelosi does get the votes for the first resolution, that doesn't make the final reconciliation bill a foregone conclusion. Sinema and other moderate senators may still want to chip away at the overall size of the package. Republicans will have the chance to offer up amendments during the final vote in September, which could whittle away at progressive priorities, as well. And Pelosi still has to ensure that the final bill is big enough to satisfy progressives without alienating the moderates, given total GOP opposition.

But that's all doable. Like I said, jigsaw puzzles aren't my favorite — but in this case, Democrats have the pieces there and ready to click together. My bet is that both bills will pass and that Biden will be able to sign them before the new fiscal year begins in October. The question is whether they look like the proverbial picture on the box at the end of this whole affair.