McConnell angered conservatives earlier this year by saying he did not want to hold another repeal vote before the November elections. But in the wake of the Supreme Court's ruling upholding the healthcare law, Republicans have tried to rally their base around repeal.
The House is scheduled to vote Wednesday to repeal the Affordable Care Act. Both chambers voted on repeal bills early in 2011, after Republicans won their House majority.
No Senate Democrats supported repeal last year. But McConnell and other Republican leaders are hoping to squeeze vulnerable Democrats with another vote now that the Supreme Court has said the health law's individual mandate is a tax.