WASHINGTON — If Mitt Romney is considering a quick pivot to the center as he heads into the general election, he will find an imposing impediment: fellow Republicans in the House.

As Congress was set to reconvene on Monday, House Republicans said Mr. Romney could go his own way on smaller issues that may help define him as separate from his Congressional Republican counterparts. But, they said, he must understand that they are driving the policy agenda for the party now.

“We’re not a cheerleading squad,” said Representative Jeff Landry, an outspoken freshman from Louisiana. “We’re the conductor. We’re supposed to drive the train.”

With Representative Paul D. Ryan’s budget plan, Republicans have already set the agenda on the key issue that divides the two parties in an age of austerity: how to manage the federal budget and its related entitlement programs. Mr. Romney has eagerly embraced it, campaigning with Mr. Ryan by his side and calling him “bold and brilliant.”