WASHINGTON  Thirty million people without health insurance stand to gain coverage under a deal announced on Saturday by Senate Democrats.

To get the 60 votes needed to pass their bill, Democrats scrapped the idea of a government-run public insurance plan, cherished by liberals, and replaced it with a proposal for nationwide health plans, which would be offered by private insurers under contract with the government.

The legislation also includes a proposal that would limit insurance coverage of abortion. The provision, which was the last piece of the puzzle to fall into place, was negotiated by the Senate majority leader, Harry Reid, Democrat of Nevada, to win the support of Senator Ben Nelson, Democrat of Nebraska, who is an opponent of abortion.

Under the agreement, states could choose to prohibit abortion coverage in the insurance markets, or exchanges, where most health plans would be sold.