WASHINGTON — The Senate voted Thursday to begin debating a $1.9 trillion COVID-19 relief bill, after Democrats made eleventh-hour changes aimed at ensuring they could pull President Joe Biden’s top legislative priority through the precariously divided chamber.

Democrats were hoping for Senate approval of the package before next week, in time for the House to sign off and get the measure to Biden quickly.

Democratic leaders made over a dozen late changes in their package, reflecting their need to cement unanimous support from all their senators — plus Vice President Kamala Harris’ tie-breaking vote — to succeed in the 50-50 chamber. It’s widely expected the Senate will approve the bill and the House will whisk it to Biden for his signature by mid-March.

The Senate’s 51-50 vote to start debating the package, with Harris pushing Democrats over the top, underscored how they were navigating the package through Congress. In the House their majority is 10 votes.

The bill will provide direct payments of $1,400 to vast numbers of Americans. There’s also money for COVID-19 vaccines and testing, aid to state and local governments, help for schools and the airline industry, tax breaks for lower-earners and families with children, and subsidies for health insurance.

The new provisions would have the government cover the entire cost of health care for some workers who lose jobs, up from its 85% share; boost spending for rural health care and capital projects; expand tax credits for student loans and start-up companies; and steer specific amounts of aid to smaller states. The details were provided by a Senate Democratic aide who spoke on condition of anonymity to describe the decisions.

Even with the late revisions, there was a good chance lawmakers will make yet another one and vote to pare back the bill’s $400 weekly emergency unemployment benefits to $300.

That potential change could also extend those emergency payments another month, through September. It was described by aides and a lobbyist who spoke on condition of anonymity to describe internal conversations.

Biden and Senate leaders had agreed Wednesday to retain the $400 weekly jobless payments included in the version of the relief bill the House approved Saturday. The reduction to $300 — which seemed likely to occur once the Senate begins a “vote-a-rama” on scores of amendments later this week — seemed to reflect a need to secure support from moderate Democrats.

It also left House Speaker Nancy Pelosi, D-Calif., the task of keeping her chamber’s numerous progressives on board. Liberals already suffered a blow when their No. 1 priority — a federal minimum wage increase to $15 hourly that was included in the House package — was booted from the bill in the Senate for violating the chamber’s rules and for lack of moderates’ support.

In another bargain that satisfied moderates, Biden and Senate Democrats agreed Wednesday to tighten eligibility for the direct checks to individuals. The new provision completely phases out the $1,400 payments for individuals earning at least $80,000 and couples making $160,000, well lower than the original ceilings.