Defense Secretary Ashton Carter “said a plan would be forthcoming,” said McCain.
Sen. Harry Reid said the GOP's spending process is "designed to fail."
Senators voted 71-25 to approve the measure which includes $38B in extra war funding.
"It's hard for me to comprehend anything so awful," the Democrat said.
Marine Corps Commandant Gen. Joseph Dunford attended the group's first meeting.
Republicans predicted a final vote will happen Thursday.
Sen. Bill Nelson had been rooting for the Tampa Bay Lightning.
John McCain wants to remove non-military medical research from the Pentagon's budget.
"This is straight out of the Republicans' playbook," the minority leader said.
The rhetorical back-and-forth comes ahead of a first test on the spending bill.