WASHINGTON — Next to the oath of office, it has been perhaps the most important commitment that Republicans in Congress can make. It is called simply “the Pledge,” and its enforcer is such a fixture in the party that he is known simply by his first name, Grover.

Signing it means a promise never, ever to vote for a tax increase.

But the pledge and its creator, Grover Norquist, a 56-year-old conservative lobbyist, have never before faced a test as they do now. The federal deficit stands at $1 trillion. The social safety net continues to grow — and, in the case of Medicare and Social Security, remains hugely popular. And unless the two parties can agree on a fiscal plan before Jan. 1, hundreds of billions of dollars of tax increases will go into effect automatically, meaning that Congress does not even need to act for taxes to rise.

The combination means that Mr. Norquist, whose long record of success is a rarity in Washington, finds himself in a tricky spot. Some top Republicans, including Speaker John A. Boehner, are saying they now agree with Democrats that the government must collect more tax revenue. Others have gone so far as to break with Mr. Norquist publicly.

By Mr. Norquist’s count, 219 House members — enough for a majority — and 39 senators have committed to the pledge. But some of those members who signed on, many of them years ago, have started to back away, apparently leaving him several votes shy of the majority he would need to block any tax increase.