Overheating the economy? Hardly. The U.S. economy was in low-gear at 1-2% growth for the last 8 years. Only this year are we likely to break 3% GDP growth again. Our historical post-WWII norm is 3-4%. The dynamic scoring of the bill shows perhaps a 0.5% GDP boost. So this "overheated economy" you characterize would actually be entirely average.
You are having a very common misconception. You have to compare growth rates in USD PPP absolut, not in percentage of GDP, if you want to compare growth in different times. So ~1.8% growth in 2017 is about as hard to get, and means as much, as 3% in 1990 and 3% in 2017 are about equivalent to 5% in 1990.
You may not know that, but even today supply is still a limiting factor and demand pull inflation is becoming a serious threat again. And that is a real killer for economies as it is inviting building up overcapacity, financed of course. You get into an oversupply situation, and that usually gets sorted out by companies going bankrupt, not being able to server their debt. We all remember how much fun mass default on credit is, right?
Lead times are already stretching, electronic components are running into shortage, even freaking passive resistors. Try sourcing tantalum core capacitors and you are looking at delivery next summer, some RAM/Flash chips have lead times between 6 and 12 month (!) by now, and that is with about double the prices from a year ago.
For a modern high GDP per capita economy, overheating happens at very low growth rates, over 2% isn´t sustainable. A dead give away for a potential overheating situation is low unemployment close to or at full employment rate, and we are well pass that. The OECD considers 4 to 6.4% unemployment rates full employment, for the US, Germany and other comparable nations 5% can be safely assumed to fit that bill. If you adjust for demographic changes economic participation rates are pretty much topped out.
In short: The FED will, and will have to, wipe out any extra growth by that stimulus package by raising the interest rate, and the whole bill is simply taking up a trillion to 1.5 trillion USD in loans and give it to the rich. Poor and middle class people will have to pay for that in higher taxes and, for many small incomes probably more important, higher interest rates. And a much bigger share of their tax revenue will go towards the debt, the compound effects from growing debt and raising interest rates are killers, instead of services/infrastructure and so on.
All of the above is why no one outside of the treasury thinks the bill will have the effects the GOP claims, and that is pretty darn obvious by the simple fact that the department published an "analysis" of the tax plan, after having hundreds of people working on it for month (!), on a single page with plenty of apparently made up numbers, as there is no explanations how they got to them. Someone should try and get their internal working papers, that "analysis" is based, on via the Freedom of Information act, and i would bet a nice little Heineken Xmas edition Magnum bottle that those internal papers say exactly what other economists say: It will add to the debt and not stimulate further growth in any meaningful way.
This signature is a safe place.