Did Senate Democrats change the frequency with which the Budget Reconciliation process can be used?
TLDR - Yes, it seems so.
This is about the procedural rules of the US Senate, which can technically be changed with a simple majority. See the nuclear option, US vs Ballin
The budget reconciliation process allows the US Senate to pass the government's budget appropriations bill with a simple majority. This is in contrast to ordinary legislation, which is subject to rules related to the filibuster.
The annual budget appropriations bill can, and often does, contain other legislation besides actual budget. Thus, in some legislative years, a large part of the year's legislation has been stuffed into a single "omnibus" bill.
Legislation in question:
This issue deals with 3 pieces of legislation. Two are the current Democratic legislative program, promised for President Biden's election.
- The "$1 trillion" infrastructure bill (originally intended to be passed in the coventional way)
- The "$3.5 trillion" everything-else package, including the social and climate-change portions of the Democratic party's legislative agenda arising from the 2020 presidential election. (intended to go into the budget reconciliation)
- Increasing the US debt ceiling, necessary to continue borrowing and funding the government into next year (subject of this question)
Context of the question:
There is some, perhaps not universal, desire to prevent the third item (debt-ceiling) from becoming entangled with the main legislative negotiation over the omnibus/budget/Biden-agenda-mega-bill. This is the context of Schumer and McConnell's discussions, from which the quote in the question comes.
Schumer's "new powers":
Finally, to answer the question. From this CBS news article
Although typically budget reconciliation is used only once per fiscal year, the majority leader asked the Senate parliamentarian whether he can revise the current budget resolution to allow for another reconciliation process to pass the infrastructure package.
The Senate Parliamentarian makes advisory rulings on matters of procedure. It has been noted that they are non-binding. Furthermore, as mentioned at the top, the procedural rules can be changed by the majority anyway, although there is resistance to doing so.