WASHINGTON — After a year of relative peace in Washington’s budget battles, President Obama will lay out a $4 trillion budget Monday that needles Republicans with proposals for higher taxes on the wealthy and businesses to pay for education, public works projects and child care.

The plan, expected to be dismissed by Republican lawmakers now running Capitol Hill, rolls out as the deficit is dropping and Obama’s poll numbers inch higher. Though Republicans will march ahead on their own, they ultimately must come to terms with Obama, whose signature is needed on anything that is going to become law.

Big challenges loom: the need to increase the government’s borrowing limit; a deadline for sustaining highway funding; a bipartisan effort to ease painful, automatic cuts to the Pentagon and domestic agencies. Those cuts are the byproduct of Washington’s previous failures to tackle the government’s deficit.

First on the agenda is the need to finalize the current-year budget for the Department of Homeland Security. It’s tied up over a Republican demand to reverse Obama’s November executive actions that extended work permits and temporary deportation relief to some 4 million people in the U.S. illegally. Funding for the department runs out Feb. 27. Obama planned a budget speech at the department Monday.

A defiant Obama challenged Republicans in his radio and Internet address Saturday.

“If they have ideas that will help middle-class families feel some economic security, I’m all in to work with them. But I will keep doing everything I can to help more working families make ends meet and get ahead. Not just because we want everyone to share in America’s success – but because we want everyone to contribute to America’s success,” he said.

Republicans insisted they are the champions of the middle class.

“Expanding opportunity, protecting middle-class savings, holding government accountable: These are your priorities, which means they are Republicans’ priorities,” said Kansas Rep. Lynn Jenkins said in the Republican response to the president’s radio address.

Obama’s plan will contain familiar prescriptions. He wants higher taxes on upper bracket earners and the oil and gas industry. He is proposing new initiatives for education and child care. He is pitching investments in roads, bridges and other projects. And he is pushing for increases for annual agency operating budgets.