For Republican officials, managing the tensions between the two parties — one official, one potent — can be something like a full-time job.

“I do spend a lot of my time running interference,” said Dick Wadhams, the chairman of the Colorado Republican Party.

“I’m a big believer in the Tea Party groups,” he said. “I’m not going to claim that every Tea Party or 9/12 leader thinks I’m hunky-dory, but I do think the people who I’ve reached out to would acknowledge that I’ve welcomed them into the Republican Party. It’s a big priority of mine.”

Some Republican Party officials say privately that they are not yet certain whether the Tea Parties will prove to be a real force or simply the loudest voices. But the Tea Parties have proven their populist rage can be a power, whether to destroy Republicans — driving one out of a special Congressional election in upstate New York — or elect them in the most surprising of places, like Massachusetts.

So publicly, Republicans are trying to make nice with Tea Party groups, particularly in states like California, Colorado, Florida, Kentucky and New Hampshire, where Tea Partiers are upending Republican unity with primary challenges to establishment candidates.