Bush was pleased that the U.S. House of Representatives failed to override his veto Thursday of "misguided legislation that would have expanded SCHIP to higher income households," White House spokeswoman Dana Perino said in a statement.

The White House was looking forward to "finding common ground" with Congress on legislation that would cover more than 500,000 children eligible for SCHIP coverage but not enrolled, Perino said.

"If enrolling these children requires more than the 20 percent funding increase proposed by the president, we will work with Congress to find the necessary money,." she said.

Bush directed Health and Human Services Secretary Mike Leavitt, National Economic Council Director Al Hubbard and Office of Management and Budget Director Jim Nussle to work with congressional leaders on a new version of the SCHIP bill, she said.