There's absolutely a problem with relative tax burden shifts from the poor to the wealthy (which is what tax cuts disproportionately for the wealthy are), independently of overall spending/tax balance.
Whether deficit spending is a problem is a completely separate question (though I'd argue that the simple "deficit = bad" position is ludicrous, current spending in excess of revenue is good or bad based on what the spending is for and what the rationally expected outcome of the spending is; sure, interest has a cost, but there are benefits to weight against that cost if the spending is well-chosen.)
The data say otherwise.
> The problem has always been deficit spending
No. In Kansas they cut spending along with taxes (no choice -- a state can't run a long-term deficit). The result has been such an unmitigated disaster that even many prominent Republicans are now supporting the Democratic candidate for governor.
The problem has always been deficit spending. That spending wasn't cut with the tax cuts; or that tax cuts weren't paid for out of surplus (which obviously the modern US Govt. has rarely had).
For example, had George W. Bush not gone on a massive spending spree, there would have been zero deficit problem during his presidency in relation to the tax cuts. The problem was the extreme spending increases during his eight years, combined with cutting revenue.
There's no inherent moral basis to claim rich people should always get soaked on taxes, even when there's plenty of revenue such that you have a surplus - it's a question of balancing.
I'd argue unchecked spending expansion, drastically faster than the rate of population increase (ie what has happened in the last 13x years), is far more destructive than tax cuts for the wealthy. If you run a disciplined budget, and an efficient government, you will more than likely be able to bring down taxes for all people over time. The US has done the exact opposite lately, as have so many other failing welfare states across the globe.