Even though Republicans have majorities in both houses of Congress, it might still be difficult for them to repeal the estate tax as they have long wished to do and as President Trump has said he would like to do. One of the biggest problems is that Republicans do not have a filibuster proof majority in the Senate. As a result, Democrats can block any ordinary legislation.
A lesser known process called “reconciliation” could be used to repeal the estate tax with only a simple majority of Senators' support. However, for that process to be used for a permanent estate tax repeal, the Congressional Budget Office must find that the legislation is revenue neutral.
As The New York Times reports in "Once Again, the Estate Tax May Die" it is not clear how the Republicans would accomplish this.
Revenue neutral means that any cuts to taxation have to be “paid for” by increasing taxes elsewhere or cutting spending. During the campaign, President Trump suggested that an estate tax repeal could be paid for by taxing all of the capital gains in an estate, but he has not proposed any legislation to do that.
It is also not certain that congressional Republicans would be in agreement with the idea.
To complicate matters, House Republicans hope to get much larger tax cuts passed on individual and corporate incomes that would also need to be scored as revenue neutral. They are having a difficult time coming to an agreement over how to pay for those cuts.
Thus, while it might appear that Republican majorities should be the end of the estate tax, in reality things are not that easy.
Reference: New York Times (Feb. 18, 2017) "Once Again, the Estate Tax May Die."