On Capitol Hill, legislators who disagree with President Obama’s legal defense of the military operation in Libya will have two options when they resume their session this week. They could try to cut off funding for the campaign, or they could formally register their disapproval that Obama did it without congressional say-so.

The first tactic has rarely worked in U.S. history.

And the second one hasn’t worked on Obama so far.

Unhappiness in Congress was magnified Saturday by a report that Obama ignored some of his legal counselors when he decided last week that the Libya campaign should not be counted as “hostilities.”

That decision allowed him to bypass the 1973 War Powers Resolution, a law that requires presidents to report to Congress on any ongoing military conflict within a limited period of time. After receiving the report, Congress then has to decide whether to authorize the action taken.

On Saturday, sources familiar with the deliberations said Obama had not overruled a formal opinion from the Justice Department’s Office of Legal Counsel — because there wasn’t one. They can take months or a year to put together.

Instead, the sources said, advisers presented him with their opinions and he chose one that White House counsel and the State Department favored.

Still, many in Congress said they were not persuaded by Obama’s logic for avoiding a congressional debate over the three-month-old conflict.

“The president has had to go through legal contortions because he knows he faces a Congress that would not give him approval,” said Rep. Michael R. Turner (R-Ohio). He has proposed a resolution that would allow Congress to formally “disapprove” of the Libya operation. “This has to be stopped,” Turner said.

This week, the Libya debate will become a key test for House Speaker John A. Boehner (R-Ohio), who appears caught between his members and his own instincts. In the House, legislators from the ideological right and left have demanded a showdown with Obama. But Boehner has seemed wary of a confrontation. When members rallied around a bill to stop the campaign this month, he authored a resolution that gave Obama 14 more days to make his case.

Obama waited 12 days. And then, on Wednesday, he told Congress he didn’t need its permission.

“U.S. military operations [in Libya] are distinct from the kind of ‘hostilities’ contemplated by” the War Powers Resolution, a White House report said.

The logic was that U.S. forces are mainly limited to supply, logistics and intelligence missions — although American drones continue to attack Libyan targets.

On Saturday, sources said Obama had solicited opinions on the matter from the Pentagon, the State Department, White House counsel and the Office of Legal Counsel, which is set up to provide independent legal analysis.

Advisers from the Pentagon and the Office of Legal Counsel, the sources said, believed that the drone strikes required that the Libya operation be described as “hostilities.” Advisers from the State Department and the White House believed they should not.

Obama, trained as a constitutional lawyer, sided against the inclinations of the Pentagon and the Office of Legal Counsel. One source emphasized this was not an illegal, or even very extraordinary, outcome.

Eric Schultz, a White House spokesman, said that “there was a full airing of views within the administration and a robust process that led the president to his view.”

On Saturday, a New York Times report describing his decision making about Libya and the War Powers act further inflamed Obama’s critics on Capitol Hill. Rep. Thomas J. Rooney (R-Fla.) said the report had convinced him that Congress ought to cut off funds for the operation.

“Today, yes, I would” support that, Rooney said. He said he was troubled by the idea that “people inside the Pentagon . . . are saying one thing but then the administration is saying something different.”

But what is Congress prepared to do about it?

On Saturday, a spokesman for Boehner said the New York Times report “reinforces the need for the White House to answer the questions that Congress and the American people have about our involvement in Libya.”

But spokesman Michael Steel was noncommittal about Boehner’s next move. “That’s something we’ll discuss” with GOP legislators, he said.

The two party leaders in the Senate, Majority Leader Harry M. Reid (D-Nev.) and Minority Leader Mitch McConnell (R-Ky.) were not available for comment on Libya on Saturday.

One option would be to hold a vote to approve or disapprove of the Libyan campaign, even if Obama has said Congress’s approval isn’t necessary.

Last week, two of Obama’s strongest allies on Libya — Sen. John McCain (R-Ariz.) and Sen. Richard J. Durbin (D-Ill.) — said they wanted such a vote. Durbin last week teamed with Sen. Benjamin L. Cardin (D-Md.) and introduced a resolution that would support the president’s Libyan actions but would set an end date of Dec. 30 and bar the introduction of U.S. ground troops, something Obama has said repeatedly he does not plan to do.

Another would be to seek to cut off funding for the operation. Rep. Dennis J. Kucinich (D-Ohio) said Saturday that he would introduce such a measure this week, when the House plans to consider a bill to fund the Pentagon.

That has happened before. In 1973, for instance, after a cease-fire had been agreed to in Vietnam, Congress voted to prohibit money being used to reintroduce troops into Southeast Asia.

In many cases, Congress has been leery about withdrawing money for troops already in harm’s way. That might still be true here, even though U.S. forces are not on the ground in Libya and face relatively little danger in the air.

Staff writers Scott Wilson, Jerry Markon, Felicia Sonmez, Walter Pincus and Ylan Q. Mui and staff researcher Julie Tate contributed to this report.