WASHINGTON — When executives from Cook Medical gathered last month to offer Representative Cheri Bustos a tour of their central Illinois medical equipment plant, they had good reason to expect a frosty reception from Ms. Bustos, a new Democratic congresswoman.

Cook executives had backed Representative Bobby Schilling, her Republican opponent in last year’s election for Illinois’s 17th District seat, after he had joined with other House Republicans to push for the repeal of a new medical device tax imposed to pay for President Obama’s health care law. The company said the tax would cut its profits this year by an estimated $15 million, perhaps limiting future expansions. But in a hint of a shift in corporate lobbying strategy now under way in Washington, the industry pitch is now focused on Democrats like Ms. Bustos.

“Republican or Democrat, we need them to understand who we are and what we do,” said Steve Ferguson, the chairman of Cook’s parent company, who was there alongside Ms. Bustos as she toured his company plant. The visit ended with Ms. Bustos telling local reporters she would consider joining the effort to repeal the tax, which is expected to raise $29 billion over 10 years.

“If current laws are holding businesses back from hiring locally, I’m open to looking into ways to improve and fix them,” Ms. Bustos said in a statement.