Investors are concerned that the setback casts doubt on whether he can push through other business-friendly tax and spending changes.
The Dow Jones slipped by 4.72 points to 20,656.53 points, while the wider S&P 500 shed 2.5 points to 2,345.96.
The tech-heavy Nasdaq index dropped 3.95 points to 5,817.69.
Shares in Ford slipped 0.9% after the carmaker said that it expected its pre-tax profits would be lower this year due to higher costs.
US shares closed little changed on Thursday, as a key debate over the healthcare bill in Congress was postponed.