WASHINGTON — As Friday night turned into Saturday morning, Vice President Mike Pence cast a tiebreaking vote in the Senate to extend a tax benefit available for higher education to families paying tuition for private elementary and secondary education — or even homeschooling their children.

The vote on the amendment by Senator Ted Cruz, Republican of Texas, was emblematic of the sweeping tax bills entering final negotiations between House and Senate Republicans. Provisions in both measures could change families’ approach to elementary and secondary education, and every type of school stands to benefit except those attended by 90 percent of the nation’s students — public schools.

Under the House and Senate bills, families who can afford to put money away for private or sectarian schools each month would be able to watch their savings earn interest and capital gains free of taxation. In the Senate bill, even home schoolers could withdraw up to $10,000 a year for school expenses in their own living room — from tax-favored savings accounts.

By contrast, the drastic curtailing of state and local tax deductions in both bills could hamstring local governments’ efforts to finance their public schools. State, county and city governments have always struggled to raise taxes or pass bond measures for schools, but were able to argue that increases in sales or income tax rates could be deducted from federal income taxes. In the House and Senate bills, the state and local tax deduction would be reduced to a deduction of up to $10,000 of property taxes each year and nothing else.