WASHINGTON — Jubilant Republicans took control of the House on Wednesday and installed Representative John A. Boehner of Ohio as the new speaker before pushing through an overhaul of House rules intended to expedite their drive to dismantle the new health care law, cut federal spending and provide the tax cuts they see as a way to jump-start the economy.

In the Senate, tensions over the partisan stalemate that dominated the last session spilled into the opening of the 112th Congress as a coalition of Democrats threatened to try to force changes that would reduce filibusters and other procedural snags that have slowed the pace of legislation the past two years.

The convening of the new Congress and the first day of divided government in Washington since President Obama’s inauguration two years ago was largely one of ceremony, posturing and such preliminary procedural skirmishes. But it set the stage for partisan and ideological clashes on the size and role of government and a wide array of other issues as the nation struggles to rebuild economic momentum, confront its rapidly growing debt and manage complex national security threats.

After accepting an oversize gavel from the departing Democratic speaker, Nancy Pelosi, Mr. Boehner promised to run the chamber in a more inclusive and businesslike way. But mindful of demands by new Tea Party Republicans for decisive action to cut spending and rein in what they see as an overactive government, he set the House on a course to take apart the health law, take a deep bite out of this year’s budget and investigate the administration’s handling of at least a half-dozen big issues over the past two years.