“Government-run health care would deprive Americans of the choice and competition that comes from the private market,” he said. “It would cause huge increases in government spending.” While the government does heavily subsidize the health coverage offered through the program, most SCHIP beneficiaries get coverage through private insurers who contract with states. That was a point stressed by Rep. Steny Hoyer, D-Md., majority leader in the House, when he provided the Democratic radio address Saturday. 160Want local news?Sign up for the Localist and stay informed Something went wrong. Please try again.subscribeCongratulations! You’re all set! The president on Wednesday vetoed legislation that would increase spending for the State Children’s Health Insurance Program by $35 billion over five years. Bush has called for a $5billion increase. Several Republicans in both chambers have sided with Democratic lawmakers on the issue. “If putting poor children first takes a little more than the 20percent increase I have proposed in my budget for SCHIP, I am willing to work with leaders in Congress to find the additional money,” Bush said in his weekly radio address. Democratic lawmakers say votes to override the president’s veto will be held in mid-October. That effort is not expected to succeed. The program provides health insurance to children in families with incomes too great for Medicaid eligibility but not enough to afford private insurance. Bush used his radio address to once again make the case that he believes the spending increase sought primarily by Democrats is a step “toward their goal of government-run health care for every American.” DEAL: The president says he’ll compromise on spending for state insurance for children. By Kevin Freking THE ASSOCIATED PRESS WASHINGTON – President Bush signaled a willingness Saturday to spend more than what he had recommended for a popular children’s health program, but provided no specifics on how much higher he would go.