The President’s FY 2018 budget asks Congress to increase defense spending over the statutory spending caps. Specifically, the President has asked for another $54 billion in new base funding for 2018. Meanwhile, the 2018 defense authorization bill signed by the President would increase defense spending by $85 billion over the statutory spending caps.
The $54 to $85 billion in new budget authority in 2018 cannot be put into base funding without amending the statutory limits on defense spending pursuant the Budget Control Act of 2011 (BCA). Furthermore, there is a point of order in the Senate on any budget resolution that supports spending in excess of that statutory spending limits (see section 312(b) of the Congressional Budget Act of 1974 (CBA)). Waiving this point of order would require 60 votes. This is why the Congressional budget resolution used for tax reform assumes current law spending on defense (the budget also includes is a "deficit neutral reserve fund" that would allow for an increase in defense spending if paid for).
However, there is a way of getting around these restrictions by using designated war funding to pay for base activities! Section 251(b)(2)(ii) of the Balanced Budget and Emergency Deficit Reduction Act of 1985 (BBEDCA) allows Congress to designate any funding that it sees fit for Overseas Contingency Operations (OCO). As long as the President also agrees with the designation (as notified by the Office of Management and Budget) the spending limits will be changed accordingly.
Many members of Congress have been critical of this approach in the past because it’s a budget gimmick (“war” funding is being used to pay for ongoing expenses that the government would incure without combat). There's another political constraint in that the OCO designation needs the support of 60 in the Senate. Therefore, to secure support, Senators would likely demand that OCO should also be increased for programs that may not be traditionally thought of as defense but still receive war funding (like the State Department). This would allow the appropriators to shift budget authority out these programs and towards other non-defense programs.
However, this is the most likely approach to increasing discretionary spending in the absence of a grand bargain to amend the BCA.