WASHINGTON — The House Republican leader said yesterday that he was prepared to vote in favor of legislation that would let the Bush-era tax cuts expire for the wealthiest Americans if Democrats insisted on continuing the cuts only for families earning less than $250,000 a year.

Speaking on CBS’s “Face the Nation,’’ Representative John A. Boehner of Ohio made clear that he supports continuing the lower tax rates at all income levels and said Democrats would be making a mistake by increasing taxes on anyone, given the weak economy.

But Boehner said that absent any other option, he would vote in favor of legislation proposed by President Obama, House Speaker Nancy Pelosi, and other Democratic leaders who want to continue the lower rates only for Americans they regard as middle class.

“If the only option I have is to vote for some of those tax reductions, I’ll vote for them,’’ Boehner said in response to questioning by the program’s host, Bob Schieffer, who pointedly asked whether Republicans were willing to hold the tax breaks for most Americans “hostage’’ to insist on continuing the lower rates for the highest earners.

As Congress returns to Washington today with lawmakers in full campaign battle mode, Democratic leaders have drawn up a daring — and potentially unrealistic — agenda for the abbreviated fall work period.

In addition to extending the Bush tax cuts for all but the wealthiest Americans, the Democratic agenda includes efforts to aid small businesses, finance the federal government until after the contentious election, and approve a new round of infrastructure spending to pump up the sputtering economy.

But with many voters angry about government spending, progress on much of that agenda is considered doubtful by some lawmakers.

Income tax cuts passed under President George W. Bush will expire at the end of this year unless Congress acts and Obama signs the bill.

The cost of extending the tax cuts for everyone for the next 10 years would approach $4 trillion, the Associated Press reported, citing congressional estimates. Eliminating the breaks for the top earners would reduce that bill by about $700 billion.

Boehner’s position on the extension, which he had not previously articulated, represents a major strategic move by Republicans, who are increasingly optimistic about taking control of the House in November.

His decision also raises pressure on Democrats, who are increasingly divided among themselves over what to do about the tax cuts.