No. You are thinking of an earlier Coburn amendment defeated on June 6th. The title of Coburn’s latest amendment says this: To require the enforcement of existing border security and immigration laws and Congressional approval before amnesty can be granted. (The word ‘amnesty’ is actually used in the title of the amendment)
This amendment gathered the support of 31 Republicans and 11 democrats. The nay vote consisted of 16 Republicans and 38 democrats. The 11 democrats were either from Red States or heavily private sector, unionized states like Michigan and West Virginia. Senator Snowe (R-Maine) also voted aye, I would bet due to her support by the shipyard workers union in Bath, Maine. Her counterpart, Sen. Collins (R) voted nay.