Short term, his plan is raise the deficit. It's possible, if GDP grows fast enough to decrease the deficit while decreasing taxes. It's extremely unlikely though and while it's often suggested as a campaign promise that growth will reduce the deficit, it's rare and essentially never backed up by the congressional budget office.
Trumps plan, which is basically the far right's plan to reducing the deficit is to (eventually) reduce mandatory spending and by cutting social security, medicare and medicaid to more manageable levels. They don't have the votes to address that now and it tends to be highly unpopular, so it's a long term game. Perhaps part of a negotiation later on, maybe when they get another surge of senators or when there's a democrat in the white-house who can share the blame. All this is a future plan, not current plan.
Politics in America is one battle at a time. Trump's current battle will increase the deficit because he wants to cut taxes. I don't think he's even formulated a strategy on reducing mandatory spending. If he has, he's not shared it publicly. When politicians say "cut social security" or "cut medicare" they get killed, so very few say it. Paul Ryan has said it, and a few others, but it's rare.
Maybe his plan is to leave it for the next guy, to cut entitlement spending or maybe he'll start talking about it (assuming he wins a 2nd term), around year 7. The unspoken truth is that there are democrats in Washington who recognize that entitlements are a spending problem and need to, at least eventually, be cut, but very few talk about it publicly. With low interest rates, the deficit is manageable and it's simply easier, for both parties, to push cutting entitlements down the line.
The big difference between the parties is the democrats want to increase taxes on the wealthy side by side with maybe, possible, at some point, enacting rarely discussed future entitlement cuts and the republicans want to take a much bigger bite out of entitlements and cut taxes.
The elephant in the room (if I haven't made this 100% obvious) is that nobody wants to suggest it first. Everyone in Washington wants to "defend" social security and medicare in appearance, even if making cuts to entitlements is something that many politicians on both sides agree that it will need to be done.
So, there it is. Trumps short term plan is to increase the deficit because tax cuts is the battle he wants to win now. Anyone who tells you that tax cuts will lower the deficit has failed basic math.
As a sidebar, while 20 trillion sounds like an insurmountable number, with low interest rates, the debt is almost manageable and could be addressed over a long period of time. The trick is getting started. To get an idea what 20 trillion feels like, the nation's total wealth fell about 20 trillion during the mortgage crisis. It's since rebounded more than that most of the money collecting in the top 1%. Our nation certainly has much more than 20 trillion net worth. The hard part is working towards a balanced budget that both sides agree on. It's easier to tax less and spend more. The real trick is responsibility. The debt is still at manageable levels.