Yes, the US is working to show strong leadership for sanctions, since the current administration fully understands the global threats to democracy posed by Russia, China, and authoritarian movements inside democracies (e.g., Hungary).
The Great Experiment — the idea that exchange and trade would bring democracy to authoritarian states — has failed so far and only empowered authoritarian states (in the medium term, at least). Authoritarian states simply found ways to route around it, and see democracy as the key threat to their existence. for example, the very existence of a free and democratic Ukraine threatens Putin's administration because the Russian people can see that one of the former USSR states being free is doing much better - raises dissatsfaction.
On the gas situation, the US cannot begin to supply enough to Europe as there are not enough ships and terminals in the world. Dependence on US gas has only slightly increased, and EU NatGas imports aren't a significant contributor to US GDP, but ARE a significant contributor to inflation. This is the last thing the US administration needs right now, and it would also be seen as a massive escalation, which the US is obviously avoiding.
Increased uncertainty today benefits only one party in the world, and that is the Russian leader.