She is also under intense pressure from the White House, where Mr. Obama has made the climate change rules a top priority — and where senior officials remind Ms. McCarthy that they are eager to avoid a repeat of the disastrous rollout of Mr. Obama’s health care law. Ms. McCarthy said she thought “all the time” about the health care rollout.

The E.P.A. is rolling out the two rules on a brisk schedule, with them timed to be completed by the end of Mr. Obama’s presidency. In September, Ms. McCarthy announced the draft of the first rule, which would limit carbon pollution from future power plants. The agency is now taking public comments on that proposal, even as experts say it has already frozen construction of new coal-fired power plants.

In June, Ms. McCarthy will unveil the draft of the second rule, which is to be an even more aggressive regulation requiring cuts in emissions at existing coal-fired power plants. Depending on how it is written, the rule could close hundreds of the most polluting plants.

Image Ms. McCarthy, the administrator of the Environmental Protection Agency, is under intense pressure. Credit... Gabriella Demczuk/The New York Times

Mr. Obama has directed Ms. McCarthy to issue a final version of both rules by June 2015, and to give states until mid-2016 to submit compliance plans.

As with the health care law, the success or failure of the regulations will largely depend on how states respond to them. While the E.P.A. will issue a broad federal standard aimed at cutting carbon pollution, each state will be directed to come up with its own plan to carry out the rules. The goal is to give each state the flexibility to devise its own plan — which also creates the risk that coal-heavy states, and those governed by Republicans who object to the climate rules, could simply refuse to put the rules in place. States might also sue the E.P.A. or find other ways to block or delay the rules.

Already, Nebraska has filed suit against the rules, and the E.P.A. anticipates that more lawsuits are on the way.