The debate became sharp at times between majority staffers and Sessions, who said they weren't providing him with clear answers.
"It does not do that, it does not come close to it," Sessions said of the $1.85 trillion figure.
"That leaves us on an unsustainable path."
Democratic staff argued on Thursday that the budget fully replaces and doesn't double count the sequester cuts with a package of alternative spending cuts and revenue increases, although Murray leaves those decisions to appropriators.
Murray argued that the since the budget does not assume that the sequester goes into place, the starting point on deficit reduction is the $2.4 trillion from the last Congress, whereas, had the sequester cuts been included, the baseline for deficit reduction would have started at $3.6 trillion.
"This is very clear," Murray said. "We're talking about a very solid plan moving forward."
She said she worked very hard to find the reductions to add to the $2.4 trillion, calling it a "pragmatic" way forward while the economy remains fragile.
Virginia Democrat Mark Warner said Democrats would be "laughed out of the room" if they assumed the $3.6 trillion figure, which, with the sequester, is considered current law.
Still, Democratic staff said Republicans could start at the $2.4 trillion figure and add the Democrats' planned replacement that matches the sequester cuts or start at $3.6 trillion and add the roughly $800 billion from other cuts, still putting deficit reduction above the $4 trillion target over 10 years.
Warner argued that while the $2.4 trillion in cuts may be a bit on the high side, he said that Murray's budget blueprint relies on assumptions made in a slew of other budget plans including Simpson-Bowles and Rivlin-Domenici and is reflective of policy discussions had by several Senate budget "gangs" in past four years.
And while the Democrats' budget eclipses the $4 trillion mark initially set as a goal more than three years ago, lawmakers should aim higher, Warner said.
But Johnson called the assumption of the $1.85 trillion in deficit reduction "false" and Sen. Crapo (R-Idaho) pointed out that there is no deficit reduction in fiscal 2014, mainly because of the budget's $100 billion in jobs and infrastructure stimulus that would start to kick in next year.
The Democratic budget achieves the reductions split evenly between spending cuts and new revenues with $493 billion in domestic cuts, including $275 billion from health savings hat do not cut entitlement benefits and will be determined by the Senate Finance Committee.
Another $240 billion comes from savings from the end of the war in Afghanistan and another $242 billion in interest savings.