Mario Rizzo points out that Keynes liked this idea.

I am converted to your proposal…for varying rates of contributions in good and bad times. (June 16, 1942). Keynes, Collected Writings, vol. 27, p. 208.

…[Y]ou are able to show fluctuations in income of an order of magnitude which is significant in the context… So far as employees are concerned, reductions in contributions are more likely to lead to increased expenditure as compared with saving than a reduction in income tax would, and are free from the objection to a reduction in income tax that the wealthier classes would benefit disproportionately. At the same time, the reduction to employers, operating as a mitigation of the costs of production, will come in particularly helpfully in bad times. (July 1, 1942). Keynes, Collected Writings, vol. 27, p. 218.

In regards to stimulus this strikes me as a good way to go. If there is a multiplier, especially for low income people this would put money into their hands, possibly very, very quickly. And since the payroll tax is a flat tax it would provide a larger stimulus for those at the lower end of the income distribution. The potential problems with this approach are that there is already a large fiscal imbalance in the programs these taxes fund. Lowering the tax rate would only make it worse, but I don’t know how much worse. Another problem is would there be the political will to either go back to the initial tax rate or even higher when the economy turns around?