With a full gas embargo, we're one polar vortex anomaly away from protests that will only favour politicians with Russian friends who are already calling for lower sanctions. In the short term this will have an effect, but unless American gas producers artificially lower their gas prices, the long term will only see more Russia-aligned politicians gaining prominence.
Europe's reliance on America and Russia has been a problem for a while and we're seeing the impact of it as we speak.
However, I do believe that "the economy" will be fine, but "the economy" mostly benefits the richest layers of society. That wealth doesn't trickle down.