It made an absolutely gigantic difference. Without the trade war, the cascades of bank failures never set off. Without that, there is a short, sharp recession in the face of the stock market crash (assuming that just happens -- it's perfectly possible that those who say Smoot-Hawley's progress through the Senate in late October was the cause of the crash are correct), and then a return to growth.
And there's very little Coolidge would be driven to do that could make him worse than Hoover.
Smoot-Hawley was a bad idea, but its effects in deepening the Depression have been *hugely* exaggerated. The article at
http://eh.net/encyclopedia/smoot-hawley-tariff/ makes the relevant points:
(1) First of all, the *extent* to which Smoot-Hawley raised rates over Fordney-McCumber had been overstated. "During the early 1930s the prices of many products declined, causing the specific tariff to become an increasing percentage of the value of the product. The chart below shows the ratio of import duties collected to the value of dutiable imports. The increase shown for the early 1930s was partly due to declining prices and, therefore, exaggerates the effects of the Smoot-Hawley rate increases..."
(2) The extent to which Smoot-Hawley led to retaliation is also exaggerated. True, some retaliation did occur that can fairly be traced to Smoot-Hawley, notably in the case of Canada. But "Clearly it is possible to overstate the extent of retaliation and Jones almost certainly did. For instance, the important decision by Britain to abandon a century-long commitment to free trade and raise tariffs in 1931 was not affected to any significant extent by Smoot-Hawley."
(3) "If there was retaliation for Smoot-Hawley, was this enough to have made the tariff a significant contributor to the severity of the Great Depression? Most economists are skeptical because foreign trade made up a small part of the U.S. economy in 1929 and the magnitude of the decline in GDP between 1929 and 1933 was so large.
"If we focus on the decline in exports, we can construct an upper bound for the negative impact of Smoot-Hawley. Between 1929 and 1931, real exports declined by an amount equal to about 1.7% of 1929 real GDP. Declines in aggregate expenditures are usually thought to have a multiplied effect on equilibrium GDP. The best estimates are that the multiplier is roughly two. In that case, real GDP would have declined by about 3.4% between 1929 and 1931 as a result of the decline in real exports. Real GDP actually declined by about 16.5% between 1929 and 1931, so the decline in real exports can account for about 21% of the total decline in real GDP. The decline in real exports, then, may well have played an important, but not crucial, role in the decline in GDP during the first two years of the Depression. Bear in mind, though, that not all — perhaps not even most — of the decline in exports can be attributed to retaliation for Smoot-Hawley. Even if Smoot-Hawley had not been passed, U.S. exports would have fallen as incomes declined in Canada, the United Kingdom, and in other U.S. trading partners and as tariff rates in some of these countries increased for reasons unconnected to Smoot-Hawley."
As for the wave of bank failures, they started in late 1930
http://en.wikipedia.org/wiki/Bank_of_United_States This was too early for the so-called trade war to have had much effect; it was for example before the British decision to go protectionist in 1931 (a measure which in any event would have taken place with or without Smoot-Hawley).
Once again, I am not saying Smoot-Hawley was a good idea--it was in fact a quite bad one IMO. But there is no evidence it had that much effect on deepening the Great Depression. And in any event, even if it did, this has no relevance to Coolidge-vs.-Hoover, because as I keep on pointing out, Coolidge was an absolutely standard Repuiblican protectionist (he even continued to defend protectionism after he left the White House) and there is no reason whatever to think he would have vetoed Smoot-Hawley.