A signature component of the health care legislation in the Senate Finance Committee is a proposal to tax expensive health insurance plans above a certain cutoff. Not only is this provision meant to help raise $215 billion toward the cost of the bill, but the Congressional Budget Office calculates that it would help slow the steep rise in health care inflation.

But the provision, to tax insurance plans costing more than $8,000 and family plans costing more than $21,000, remains controversial. It will be the subject of numerous amendments in the Finance Committee this week, in part because of reservations among lawmakers from some of the states where health-insurance costs are highest — and where the new tax presumably would hit hardest. (The tax would be 35 percent on the amount over the cutoff.)

To allay these concerns, the committee chairman, Senator Max Baucus, Democrat of Montana, has proposed a transition period, during which the cost threshold of plans subject to the tax would be increased temporarily in 17 states with the highest health care costs. In 2013, the first year of the tax, the amounts would be increased by 20 percent; in 2014 by 10 percent in 2014; and in 2015 by 5 percent. In 2016, the threshold would be the same everywhere.

But this proposal struck Senator Orrin G. Hatch, Republican of Utah, as unfair — presumably because of the likelihood that the transition would benefit states like New York, New Jersey and California where the cost of insurance is higher than in his own.

So Mr. Hatch has proposed an amendment that would extend similar “transition relief” to any state with a name that begins with the letter U.

“The transition relief provided in the chairman’s mark for the 17 states with the least affordable health care is obviously arbitrary and unfair,” Mr. Hatch wrote, explaining the rationale for his amendment. “What about the 18th state? This amendment would add further transition relief in another, but no less arbitrary way to certain states.”