Both, or nothing
By 
JMM is correct that if Sinema refuses to agree too pass the BBBA, House progressives should refuse to pass her vanity bipartisan infrastructure act:
I had a conversation yesterday similar to a number I’ve heard over recent days: a business lobbyist explaining that yes, they want the infrastructure bill real bad and that their optimal scenario is that the infrastructure bill passes and the reconciliation bill goes down to defeat entirely. A separate irony is that most of those people – the ones who appear to have Sinema’s ear – seem entirely unable to grasp the implications for the Democratic party if that is indeed the final outcome. It will rip the Democratic coalition apart. Of course, in general, that’s not their concern or their problem. But it certainly means all the self-styled “moderates” they’re working with now will go down to defeat – both because of primaries but also just as the natural consequence of a Democratic rout. More business friendly Democrats in blue seats will also get replaced by more progressive members. I am consistently surprised how people whose whole job is politics, supposedly, seem to have so little grasp of its basic functions.
[…]
It is perverse and bizarre since the Democrats, though tenuously, now have unified control of the government rather than being a beleaguered opposition with no holds on any levers of power. How we’ve gotten to the point that they cannot collectively control the outcome … well, that’s crazy. But that’s where we are. Largely because of Kyrsten Sinema. But look at what we’re talking about here. Is the reward for her betrayal having the party she is betraying pass her infrastructure bill? That’s too crazy to allow to happen. It is a basic element of life for individuals that we must strive to confront with dignity things we cannot control. It shapes who we are. And something similar applies to political coalitions and parties.
Now there are potentially lots of ways to skin this cat. Maybe the House passes the bill but Speaker Pelosi declines to send it to the President until there’s movement on the reconciliation bill. Or the President would hold it for a week himself. As has been the case throughout this maddening year there are just too many factors that aren’t visible to us. Democrats will have to rely on Nancy Pelosi and others to make good decisions based on knowledge of details they cannot share. But to the extent we can be clear on goals, to the extent we must shape transitory tactics with a clear understanding of where we want to end up, a final outcome that is an infrastructure bill and nothing else is just not tenable. It leaves too many critical priorities unaddressed – especially climate – and makes a mockery of the whole Democratic coalition.
If it’s the BIF and nothing else, kill the BIF.
Despite what the moderates and a lot of their media cheerleaders seem to think, the mediocre highway bill isn’t a once-in-a-generation opportunity to entrench a major social reform, like the ACA, giving progressives no real option to walk away. It’s expendable; BBBA is the one that matters, both substantively and politically. Passing BIF alone will not move the needle in 2022 and 2024:
It's the difference between finishing 0-16 and finishing 1-15. What would strengthen absolutists is electing Biden and showing the Democratic party can't advance any progressive goals: not health care, not child care, not education, safety net.— Jonathan Chait (@jonathanchait) September 29, 2021
This is a relatively rare case where the leverage is with the progressives; the Narcissist Caucus cares way more about the highway bill than anyone else. They can accept the original deal and vote to pass both bills or they can renege and get nothing. Their choice, but as JMM the reward for betrayal can’t be that the betraying faction is the only one that gets what it wants.