WASHINGTON — Recognizing that a weak economy still needs a government boost, the Senate voted overwhelmingly Wednesday to provide the jobless with up to 20 weeks in additional unemployment benefits and expand a first-time homebuyer tax credit to include a far larger pool of people entering the dormant housing market.

The $24 billion bill, passed 98-0, also provides tax relief for struggling businesses. It comes to the rescue of more than 1 million out-of-work people who will run out of benefits by the end of the year. Everyone will receive 14 weeks of additional benefits, while those in states with unemployment rates of 8.5 percent and above get six weeks on top of that.