WASHINGTON — A sweeping vote by conservative Republicans controlling the House and President Barack Obama’s Democratic allies has sent a bipartisan budget agreement to the Senate, where it will encounter stronger but probably futile resistance from the GOP.

The modest package passed by the House would ease the harshest effects of another round of automatic spending cuts set to hit the Pentagon and domestic agencies next month. Supporters of the measure easily beat back attacks on it from conservative organizations that sometimes raise money by stoking conflict within the Republican Party.

Democrats who were upset that the bill does not extend jobless benefits for the long-term unemployed suppressed their doubts to advance the measure to the Democratic-led Senate, where Obama’s supporters appear set to clear it next week for his signature.