Neither Republicans nor Democrats are being spared in the minds of voters, one said. “They blame ‘the government,’ ” said Ms. Collins, who noted that many Maine residents were panicked at the possibility of paying $5,000 to heat their homes this winter.

She and other lawmakers said they could see the contours of a deal that included new incentives for renewable fuels, more freedom for drilling in waters off states that sanction the drilling and a potential crackdown on speculation in the oil-futures market.

In both parties, there was a notable shift in tone.

Senator Harry Reid of Nevada, the majority leader, has made a refrain in recent weeks of saying, “We cannot drill our way out of this problem.” But he opened his news conference on Tuesday with a different approach: “Let’s begin the discussion here by saying, Democrats support domestic production.”

He also hinted at a potential element of compromise legislation: that any oil produced from wider access to federal lands off shore be reserved for domestic use and barred from export. At the same time, he noted that Senator John McCain of Arizona, the Republican presidential candidate, had opposed similar restrictions in the past.

There was no indication from Mr. Reid or other lawmakers that a deal was imminent. And lawmakers acknowledged that none of the proposals under consideration would lower gasoline prices any time soon.

Republicans continued their call for expanded oil drilling, while emphasizing their willingness to compromise.

“When I was in Texas this last week, this is the No. 1 issue on people’s minds,” Senator John Cornyn said. “When people fill up their trucks or S.U.V.’s in Texas and pay over $100 to fill up their vehicle, it gets their attention, and they are looking to Congress to frankly get out of the way and allow America to develop more of its own natural resources as we take other measures to conserve energy and become more efficient.”