Don't make the mistake Republicans made when they ran all three branches of government. Make Republicans feel like fellow Americans with a different plan for reaching similar goals. No one wants poorly performing schools, more poverty and a weak national defense. If we can agree on the problems, we can then discuss the best way to solve them. Include Republicans in your decision-making and at least occasionally embrace some of their ideas. Disarming your opponents is less bloody and can be more productive than crushing them. Most people are tired of the partisan bickering. If you produce results through a common ground approach, as you pledged to do during the campaign, you will engender goodwill. Goodwill is the capital every president must have to get anything done.
I realize this next suggestion is self-serving. Invite conservative columnists and opinion leaders in to see you. Explain to them what you are doing and consider their ideas for doing it better (or not at all). This, too, is likely to generate goodwill among some who could quickly be an impediment to your success. We conservatives don't want to be saying "no" all the time and that personality of yours might just win some of us over; if not on all of your policies, then at least on some. Fortunately, you made a good start here by recently meeting with conservative columnists who have been critical of you in the past. More of this is needed.
You may think you are all-powerful (or others may tell you that) but don't let "the smell of the white paint," as a friend who worked in the Nixon administration called it, intoxicate you. Humility is a strong quality that contrasts with the arrogance and hubris so often associated with the city in which you will temporarily reside. Work hard on thinking of others as better than yourself. In doing so, you might humble some of them, which would be a miracle in itself.
Good luck, God bless and I hope you succeed in the things with which conservatives can agree. And on those things we cannot agree, I at least promise to be more than a naysayer and suggest how they might be done better.