Debt ceiling doesn’t have to be handled in the same bill as Build Back Better; it can be addressed through Reconciliation as a stand-alone bill.
Sen. Roy Blunt said that what the Republicans are looking for with forcing the effort through Reconciliation is a number. Via Reconciliation, the number to which to raise the debt ceiling has to be specified so that it can be scored for Reconciliation. This will enable them to point to the new number and decry the evil of Democrats raising the debt to some horrible number, all in an effort to pay for what the Republicans have already spent.
The Democrats are trying to temporarily waive the debt ceiling, as was done several times during the Trump administration, and not specify a new ceiling. This cannot be done through Reconciliation.