First of all, note that nine and only nine would sign on to this letter.
That is not a large number.
Second, note that they do not analyze the deficit-increasing tax bill on display, but rather something else:
Robert J. Barro, Michael J. Boskin, John Cogan, Douglas Holtz-Eakin, Glenn Hubbard, Lawrence B. Lindsey, Harvey S. Rosen, George P. Shultz, and John. B. Taylor: How Tax Reform Will Lift the Economy: "In the foregoing analysis, we assumed a revenue-neutral corporate tax change...
Third, note that they do not model and calculate but rather assert that changes in interest rates" will be small because "the United States operates in an international capital market":
...Deficit financing... increases federal debt and interest rates, all else equal. For the House and Senate Finance bills, this offset is likely to be modest, given that the United States operates in an international capital market, which means that the impact of changes in interest rates resulting from greater investment demand and government borrowing are likely to be relatively small...
Fourth, note that that assertion is wrong. The U.S. is not a small open economy. The U.S. is more than 1/3 of the international financial economy, so that long run world average interest rates will rise about 1/3 as much from bigger U.S. deficits as they would if the U.S. are a closed economy. And even in small open economies interest rates deviate substantially from the averages of the international capital market. International capital and goods mobility is far from perfect: we have known this for fifty years, and for fifty years standard modeling has produced large swings in exchange rates, trade flows, and domestic interest rates in short and medium runs that extend well beyond a decade.
Fifth, note that while they claim that "the impact of changes in interest rates will be "small", the metric they use to claim that the drag on growth from larger deficits will be small also labels the boost to growth that they see "small" as well. They see a 3% boost to GDP from lower capital taxes. From that you need to subtract a 1.5% reduction in GDP from deficit drag. You get a final 1.5% boost to GDP according to their modeling strategy if you do not sweep the deficit effects on saving under the rug
Sixth, note that that 1.5% boost is a boost to GDP, not to national income. By the time you have subtracted off the fact that foreigners will be paying less taxes to the U.S. Treasury, the effect on national income is in the range of zero.
Seventh, note that while they say that growth effects would "reduce the 'static cost' of the reforms', they do not say that it would reduce the "static cost' by much.
Unwillingness to quantify the dynamic offset on revenues, unwillingness to acknowledge the wedge between national income and domestic product, unwillingness to quantify the deficit drag on growth, simply wrong on the consequences of cross-border finance and trade, unwillingness to quantify what their (wrong) approach thinks the consequences of cross-border finance and trade are, unwillingness to actually analyze the bill at hand rather than something else, and inability to get more than nine economists to sign on—this is a document that documents, above all, the unwillingness of even highly partisan Republican economists to get on this particular train in any way that might produce pushback from their less-partisan peers.
Thus the way to understand this letter is to understand that its writing and publication has three goals:
The first point is to get at least some economists on record saying something that will be interpreted by Fox News and others as: "some economics say that the bill will provide a big boost the economy and also almost pay for itself".
The second goal is to avoid having to get even those some economists on record actually saying that the bill will provide a big boost the economy and also almost pay for itself.
The third goal is to thus get CNN and the New York Times out there saying "economists differ".
If you want a Republican economist's take that will actually inform you, you should go to Greg Mankiw: he is correct in his description of the current process and bill as being an "unworkable mess".