Washington ? The Senate voted Thursday to give some low-income families a check worth up to $400 for each of their children, as Republicans buckled under demands from Democrats to make more low-wage workers eligible for an increased child tax credit.

“These are hardworking couples who put in a hard day’s work,” said Democrat Blanche Lincoln of Arkansas, who pressured Republicans to revisit the tax cut President Bush signed in May. “They’re trying desperately to raise a family.”

The Senate’s overwhelming 94-2 vote in favor of the tax package, which expands the child credit for low-income workers and high-income married couples, underscored the political momentum building behind the issue. The only two senators to oppose the legislation were Republicans James Inhofe and Don Nickles, both of Oklahoma.

The tax package must reach the president’s desk by June 23 for low-income families to get checks along with 25 million middle-income households already slated to get an advance refund of the child tax credit, just temporarily increased to $1,000.

“I’d like to see all of these folks included when the round of checks are sent out this summer,” said Senate Finance Committee Chairman Charles Grassley, R-Iowa.

But before workers can count on the money, the House must pass the bill. House Republican leaders — cool to sending payments to workers who pay no income taxes — have not said whether they would consider the legislation.

Some Republicans have historically supported refundable tax credits, such as the much larger earned income tax credit, as a way to encourage low-wage workers to stay in the labor force and avoid welfare.

But this year’s debate saw Republicans arguing that tax cuts should lift the burden on those who pay income taxes.