But budget agreement requires veterans under 62 to pay more into their retirement accounts.
McConnell criticized Reid for pushing the Defense authorization bill without amendments.
They are trying to defuse anger over the move to rush through the $607 billion Defense bill.
The race is on to finish the Defense authorization bill.
Lawmakers won't have time to consider amendments if it is to be finished this week.
House, Senate members will present details of a final Defense authorization bill on Monday.
Defense hawks want end to sequester, but conservatives want cuts.
House Armed Services Committee Chairman Buck McKeon (R-Calif.) said Thursday he was “confident” that Congress would pass the stalled Defense authorization bill this year.
But to do so, the Senate may have little chance to consider significant amendments on the bill.
Rep. Adam Smith said lawmakers will use procedural maneuver to ensure the bill is passed.
House Armed Services Committee Chairman Buck McKeon (R-Calif.) returned fire at the conservative Wall Street Journal editorial board on Thursday after it accused him of leading an “insurrection” over raising the sequester-level budget caps.