Sources say the players will submit a new formal proposal Tuesday, and the owners are expecting it to represent enough of a shift in their position to warrant further negotiation.

That's what Stern meant when he said last week, "Tuesday is a very important day in these negotiations."

Sources say the players' most recent proposal included an offer to accept less than 50 percent of additional revenues beyond a certain point in the new CBA. For example, revenues are expected to come in at close to $3.8 billion when the books are completed on the 2010-11 season, so the players essentially proposed keeping their current 57 percent of BRI (basketball-related income) up to that threshold while giving the owners more than 50 percent on revenues beyond that. The owners have yet to move off their insistence on excluding about $900 million of revenues from the players' share and a 50-50 split after owners pocket the difference.