President Bush and Congress’s newly empowered Democratic leaders alike are expressing hope for bipartisan cooperation that could lead to a minimum wage increase, an immigration law overhaul, and perhaps even changes to Iraq policy.

As the likelihood of Democratic control of the Senate grew greater yesterday and the size of the Democratic majority in the House became clear, Mr. Bush used a White House press conference to reach out to Democrats on a variety of policy issues. He spoke of the way he had cooperated with Democrats early in his first term to pass a law expanding federal education funding in exchange for increased accountability.

“The No Child Left Behind Act is going to come up for reauthorization,” Mr. Bush said. “There’s an area where we must work together for the sake of our children and for the sake of a competitive America.”

Mr. Bush also mentioned the immigration issue as another opportunity for bipartisan cooperation. Mr. Bush ran into resistance this year from Republicans in Congress over his plan for a guest worker program. Many Democrats, however, supported the measure, and Mr. Bush said he hoped to work with them on this issue again.

“There’s an issue where I believe we can find some common ground with the Democrats,” Mr. Bush said. “When you’re talking comprehensive immigration reform, one part of it is a guest worker program, where people can come on a temporary basis to do jobs Americans are not doing.”

Mr. Bush also spoke of a minimum wage increase as an area where he believes he can “find common ground” with Democrats, though he said he wanted to make sure “small businesses” are compensated as part of any legislation to increase the minimum wage.

Democrats, for their part, basked in their victories and stopped short of frontally challenging the White House on core issues.

“We’re not going to raise taxes,” Senator Schumer, the chairman of the Democratic Senatorial Campaign Committee and a member of the Finance Committee, told Fox News Channel’s “O’Reilly Factor.”

Rep. Charles Rangel, the Democrat from Harlem who is set to become chairman of the Ways and Means Committee, said that while he disagreed with Mr. Bush’s tax cuts because they benefited the wealthiest Americans, concerns that Democrats would reverse the tax cuts immediately were unfounded.

“These tax cuts, which I have vigorously opposed, don’t expire until 2010. It seems to me as a legislator that it doesn’t make any sense at all, indeed it would be irresponsible, to dictate what we will be doing on the tax writing committee when we have no idea what the economy is going to look like in 2010, ” Mr. Rangel said at a press conference yesterday in New York.

Mr. Rangel said the estimated $345 billion tax gap between what is owed and what is paid needs to be closed. He said funding to the IRS has been cut drasticallyin recent years and that as chairman he will make sure the agency gets the resources it needs to collect unpaid taxes.

Mr. Rangel also said that ending tax shelters for companies that move jobs overseas was a top priority. In addition, Mr. Rangel said his committee would also attempt to provide relief for those middle class taxpayers hit by the alternative minimum tax. The alternative minimum tax is particularly likely to affect taxpayers in states like New York, where both housing costs and state and local taxes are high, leaving taxpayers with large federal tax deductions.

To get all of this accomplished, Mr. Rangel reiterated the Democrats’ pledge to reach across the aisle.

“There is no Democratic solution to the starvation of social security. For Medicare. To reforming the tax code and certainly not to getting our troops out of Iraq. But one thing is clear is that we can’t do it alone. The only way to resolve the problems is by working with the Republicans,” Mr. Rangel said.

On Iraq, Senator Reid, who is in line to become majority leader if the Democratic victory in the Senate race in Virginia holds, said in a statement, “I ask the President to convene a bipartisan Iraq summit with the leaders of Congress and the chairman and ranking members of key national security committees. After more than three years of a failed strategy, we must come together to change course and give the American people and our troops the real security they deserve.” Mr. Reid said.

Mr. Bush said, “I and members of my national security team will meet with the members of both parties to brief them on latest developments and listen to their views about the way forward.”

Mr. Bush said that the incoming speaker of the House, Rep. Nancy Pelosi of California, will be visiting the Oval Office later this week. And while he expressed optimism about the possibilities of cooperation, he also acknowledged its limits.

“I believe on a lot of issues we can find common ground,” Mr. Bush said. “And there’s a significant difference between common ground and abandoning principle. She’s not going to abandon her principles and I’m not going to abandon mine.”