The White House is rushing to come up with an unspecified fix as early as this week to counter the millions of health coverage cancellations going to consumers, at the same time it promises improvements in a federal website so balky that enrollments totaled fewer than 27,000 in 36 states combined. Adding in enrollment of more than 79,000 in the 14 states with their own websites, the nationwide number of 106,000 October sign-ups was barely one-fifth of what officials had projected — and a small fraction of the millions who have received private coverage cancellations as a result of the federal law. Administration officials and senior congressional Democrats expressed confidence in the program's future. Despite the expressions, the White House raced to reassure anxious Democrats who are worried about the controversial program, which they voted into existence three years ago over Republican opposition as strong now as it was then. Across the Capitol, majority Republicans in the House set a vote for Friday on legislation to permit insurance companies to continue selling existing policies that have been ordered scrapped because they fall short of coverage standards in the law.