WASHINGTON — In a deepening struggle over spending, Republicans and Democrats swapped charges Thursday over a possible government shutdown when money runs out March 4 for most federal agencies.

“Read my lips: We’re going to cut spending,” declared House Speaker John Boehne

r. He pledged that the GOP-controlled House would refuse to approve even a short-term measure at current funding levels to keep the government operating.

The Ohio Republican prefaced his remarks by accusing Democrats of risking a shutdown “rather than to cut spending and to follow the will of the American people.”

But moments later, Senate Majority Leader Harry Reid, D-Nev., retorted that Boehner was resorting “to threats of a shutdown without any negotiation.” Officials added that Democrats would seek a short-term bill without any cut in spending levels, a position sharply at odds with Boehner’s.

The sparring occurred as the House labored to complete work on veto-threatened legislation to cut more than $61 billion from the budget year that’s more than a third over. That bill also would provide funding to keep the government operating until Sept. 30.

Working through dozens of amendments, the House voted 244-181 in early evening to block the FCC from implementing “network neutrality” regulations. The rules prohibit phone and cable companies from discriminating against Internet content and services, including online calling and Web video services that may compete with their core operations.

With that one bill at the center of a political dispute — the House has repeatedly worked well past midnight on the legislation this week — Boehner chose the moment to open a second front. To underscore the budget-cutting commitment by the 87 conservative new members of his rank and file, he announced that Republicans would move quickly this spring on companion legislation to cut “wasteful mandatory spending” by the federal government.

He provided no details, but party officials said they expected the effort to begin shortly after the House returns from next week’s recess.

The current legislation is sweeping in scope, containing cuts to literally hundreds of domestic programs, from education to environmental protection, nutrition and parks.

In addition, it has become a target for first-term conservative Republicans eager to demonstrate their budget-cutting bona fides and for other lawmakers hoping to change the course of government in ways large or small.

Republicans led the way on a 250-177 vote to stop the Environmental Protection Agency from imposing limits on mercury pollution from cement factories. Supporters said the new rules would send American jobs overseas.

An attempt by Democratic Rep. Barney Frank to increase funding for the Securities and Exchange Commission was turned back, despite arguments that lax enforcement of Wall Street contributed to the financial meltdown of two years ago. The vote was 270-160.

Controversial social issues also came into play.

Rep. Mike Pence, R-Ind., a strong foe of abortion, proposed to block Planned Parenthood from receiving any federal funds. The organization provides a variety of women’s health services, and its website says abortion is a “safe and legal way to end pregnancy.”

Critics of the proposal noted that federal law already prohibits the use of government funds for abortions in most circumstances.

House leaders had originally hoped to complete work on the bill by day’s end, but even after long hours in session this week, that appeared increasingly unlikely.

Among the dozens of proposals yet to be voted on was an attempt to block the use of funds to implement the year-old health care law, and a move to prevent the Federal Communications Commission from implementing proposed new regulations known as network neutrality.

At 359 pages, the legislation would eliminate some programs while reducing many more.

Among those targeted for elimination are the Corporation for National and Community Service, which oversees AmeriCorps and Senior Corps and currently has a budget in excess of $1 billion.

Funding for the Corporation for Public Broadcasting would also be wiped out, at $86 million.

The spending bill bears the strong imprint of the newly elected Republicans, many of whom were backed by tea party supporters and are sworn to reduce deficits.

An attempt by GOP leaders to send a smaller package of spending cuts to the floor was rebuffed last week by the newcomers, who said they would accept nothing less than a measure that met their commitment to the voters last fall. As candidates, they promised to cut Obama’s budget request by $100 billion, a figure that translates to $61 billion from current levels.

While passage in the House is assured, the legislation faces a rocky reception in the Democratic-controlled Senate. Democrats there have not yet said what level of cuts, if any, they will accept through Sept. 30. Nor has the White House.

As a result, the expectation is widespread that no final compromise will be reached before the March 4 deadline, leaving lawmakers and the White House to work out a stopgap bill — or perhaps even a series of them — while negotiating over the comprehensive measure.