Rep. Liz Cheney, R-Wyoming, promised neither she nor the Republican-dominated Congress will abandon those with health insurance purchased under the Affordable Care Act, she said Wednesday.

"You have my absolute commitment that I'm certainly not going to support anything that will kick people off of the care they have now," Cheney said at an informal meet-and-greet event at her office in the federal building in downtown Casper.

"I think that's a commitment you've heard certainly from the Republican leadership in Congress that we're not going to pull the rug out from under people," she said.

Cheney was responding to a question by Casper resident Pat Pulitzer, who is on a fixed income two years after her husband died and was able to buy health insurance through the insurance exchange under the Affordable Care Act, otherwise known as Obamacare.

Pulitzer wondered what's next, she said. "My concern is what specific plan is place."

Earlier this week, Cheney and the majority of the U.S. House voted largely along party lines for a process called “budget reconciliation” to be used in order to carve out major elements of the Affordable Care Act.

“I am proud that one of my first votes in Congress was to start the process to repeal and replace this failed system,” Cheney said in a statement. “The people of Wyoming deserve healthcare that puts patients and their families in the driver’s seat.”

Wednesday, she said, "You hear a bunch of people in Washington talking about repeal-and-replace, and you know, we're talking about your life."

Pulitzer said she gets the "repeal" part, but not the "replace" part.

"I keep hearing, 'it's going to be great; it's going to be this; it's going to be that,' but there's been nothing to replace," she said. "I realize it's not a perfect system, but I have managed to have health care and I'm really afraid that I'm not going to have health care soon."

About 25,000 people in Wyoming have signed up for health care in exchanges under the Affordable Care Act, and Cheney said any replacing needs to keep some of its basic components and add others.

"One of those is pre-existing conditions, the other is portability so that when we're in tough economic times and people lose their jobs they also don't lose their health insurance," Cheney said. "The other thing that's crucial is that people be able to buy insurance across state lines."

A replacement also must enable people to be in charge of their own health care decisions," she said. "So in my view  one of the most effective way to do that is to force insurance companies to compete."

Wyoming has its own set of health care and health insurance issues because the state is so rural, she added.

After the meet-and-greet, Pulitzer said she's not necessarily confident in Cheney's response.

"I feel that Ms. Cheney told us what she thought we wanted to hear," Pulitzer said.

"While she appeared to be sincere, (she) gave me nothing solid to base my hope on for a reasonable replacement of the ACA," she said. "She said they would not 'pull the rug out from under' us, and I intend to hold her to her word."