The election left Democrats in Congress scrambling to salvage a bill overhauling the nation’s health care system, which the late Mr. Kennedy had called “the cause of my life.” Mr. Brown has vowed to oppose the bill, and once he takes office the Democrats will no longer control the 60 votes in the Senate needed to overcome filibusters.

Image A supporter of Scott Brown waved a flag after the Senate election results were in. Credit... Robert Spencer/Getty Images

There were immediate signs that the bill had become imperiled. House members indicated they would not quickly pass the bill the Senate approved last month.

And after the results were announced, one centrist Democratic senator, Jim Webb of Virginia, called on Senate leaders to suspend any votes on the Democrats’ health care legislation until Mr. Brown is sworn into office. The election, he said, was a referendum on both health care and the integrity of the government process.

Beyond the bill, the election of a man supported by the Tea Party movement also represented an unexpected reproach by many voters to President Obama after his first year in office, and struck fear into the hearts of Democratic lawmakers, who are already worried about their prospects in the midterm elections later this year.

Mr. Brown was able to appeal to independents who were anxious about the economy and concerned about the direction taken by Democrats, now that they control both Beacon Hill and Washington. He rallied his supporters when he said, at the last debate, that he was not running for Mr. Kennedy’s seat but for “the people’s seat.”