In a letter to colleagues, Mr. McConnell and Mr. Lott said that the measure “imposes an open-ended financial burden on American taxpayers and takes a significant step toward a government-run health care system.”

Six Republicans voted for the bill. Mr. McConnell said other Republican senators were concerned about “the size of the plan that came out of the Finance Committee and what that may portend for the future in terms of an entire government takeover of American health care and, in essence, a single-payer system down the road.”

Representative Diana DeGette, Democrat of Colorado, a leading proponent of the House bill, said: “For the longest time, I was mystified why Republicans would oppose expansion of the Children’s Health Insurance Program to kids who are eligible but not enrolled. Now I realize. They are trying to deny us a political victory. They want to be able to say that Democrats can’t get anything done.

“Unfortunately,” Ms. DeGette said, “Republicans are pursuing this strategy on the backs of poor children.”

The Senate bill focuses on coverage for children. The House bill also calls for major changes in Medicare. It would, for example, halt a 10 percent cut in payments to doctors, scheduled for January, and would reduce payments for private insurance known as Medicare Advantage plans. Medicare typically pays the private plans more than it would cost to care for the same people in traditional Medicare. Many private plans offer additional benefits.

America’s Health Insurance Plans, a trade group, announced a national television advertising campaign. The ads will urge older people to contact their members of Congress and speak out against the proposed cuts in payments to private insurers.