There are 3 types of bills that are eligible for using the reconciliation budgetary process - one that deals with revenue (taxes), one that deals with spending, and one that deals with the debt. Each of these 3 types can only be used once each FY, and can be standalone or combined into 1 or 2 separate pieces of legislation.
They have already used the "spending" reconciliation option this fiscal year for the "American Rescue Plan" (the stimulus thing that was signed into law at the end of April of this year).
Therefore they can't use that option again for the Infrastructure bill this fiscal year. They have to wait until next fiscal year (FY22), which literally starts October 1st, 2021.
So that is why the talk about "months and months".
August starts this Sunday and so you have the whole month of August and the whole month of September before you can even introduce something like that. And even then, since September 30 is the end of the FY and there is a need for funding the government for FY22, they are going to be tied up in that process of probably doing a CR (continuing resolution), potentially resulting in a Ted Carnival Cruise-syle government shutdown.
So they want to get some base package drafted (that requires cloture) and then see what is needed later to do any supplemental funding instructions for it using a 2nd package through reconciliation (which is the PITA due to Manchin, Sinema, and probably some others who don't do circus floor shows for attention like Chris Coons).
Because the power of the purse resides with the House, the Senate has to do all of this using some House-passed legislation, and then they work the amendments on it as a "substitute" and have the House accept that as "their version".