It finally looks like Republicans and Democrats on Capitol Hill are ready to agree on something related to the uprising in Libya. All it took was for the revolt to succeed, longtime dictator Moammar Gaddafi to be captured and killed and American involvement to end.

On Tuesday, the Senate Foreign Relations Committee is to consider a resolution, sponsored by Chairman John Kerry (D-Mass.), along with Sens. John McCain (R-Ariz.) and Joseph I. Lieberman (I-Conn.), applauding Libyans for their successful rebellion and U.S. troops for their “bravery.”

“This resolution is about honoring the courageous people of Libya as they begin to rebuild their country,” Kerry said. “It’s an affirmation of bipartisan support for their democratic aspirations.”

The language may sound innocuous, but nothing about the Libya debate has been easy so far.

This summer, lawmakers from both parties squabbled with each other and the White House over the wording of a series of resolutions to approve or disapprove of the U.S. military’s role in the NATO mission in Libya.

In June, Kerry and McCain introduced a resolution authorizing the limited use of U.S. military forces in Libya. The bill was defeated in the House by a wide bipartisan margin, and it never came up for a vote in the Senate.

But on the same day that bill failed in the House, the chamber also voted down a measure that would have cut funding for American operations in Libya. That left the U.S. mission in a form of legislative purgatory — with Congress upset enough to criticize Obama’s handling of the mission but not so angry as to actually pull the rug out from under it.

Then Congress’s indecision was overtaken by events. Tripoli fell to Libyan rebels in August, and Gaddafi was killed Oct. 20. The NATO mission officially ended Oct. 31.

Now the Senate may be ready to act.

The Foreign Relations Committee resolution “congratulates the people of Libya for their tremendous courage and extraordinary resilience in liberating themselves” and “commends the men and women of the United States Armed Forces and their coalition partners who engaged in military operations to protect the people of Libya for their extraordinary bravery and professionalism.”

The resolution also “affirms the national interest of the United States in a successful and irreversible transition to democracy in Libya.”

Will the new measure earn the full support of the Foreign Relations panel, or will it split lawmakers like the June bill did? The last version was opposed by Sen. Richard G. Lugar (Ind.), the committee’s top Republican. Lugar’s spokesman said Monday that he had not seen the final version of the new bill yet.

Across the Capitol, the House is to vote this week on a constitutional amendment requiring a balanced budget, a top legislative priority of nearly every congressional Republican and some Democrats.

The measure, sponsored by Rep. Bob Goodlatte (R-Va.), will be the first constitutional amendment on the budget or any other topic to actually get a floor vote in the House or Senate this Congress. Other lawmakers have been unsuccessful so far in bringing their amendments to the floor, but not for lack of trying.

Goodlatte’s is just one of 68 constitutional amendments that have been introduced this Congress, spanning a wide range of topics.

Some are duplicates — the same bill offered in both the House and Senate — and others are slight variations on each other. There are at least 15 versions of the balanced budget amendment in the House alone, and another handful that would “control federal spending.” Some of those bills are identical too, but they give their sponsors — particularly freshmen Republicans looking to burnish their resumes — the chance to brag that they “authored” such a measure.

The Budget Control Act, which passed in August, required that both the House and Senate vote on a balanced budget amendment. In March, 58 senators voted in favor of a non-binding resolution supporting the idea of such an amendment.

Beyond the budget, several members want to limit the number of terms members of Congress can serve, while Rep. José E. Serrano (D-N.Y.) wants to lift the two-term limit for presidents. Rep. Jesse L. Jackson Jr. (D-Ill.) has offered a host of amendments guaranteeing the right to quality education and health care, among other subjects.

An amendment prohibiting same-sex marriage is a perennial offering, as is one prohibiting flag-burning. Some lawmakers also want to allow for the nullification of federal laws if they are opposed by two-thirds of the states.

As eager as members have been to offer amendments, they’re not moving at any faster pace than in past years. In the 111th Congress, lawmakers offered 77 such amendments, and they introduced 66 in the 110th.

The pace pales in comparison to that of the early 1990s, when members regularly offered more than 150 amendments every two years, according to numbers provided by the Senate Library.

But they weren’t much more successful then than they are now. The last amendment to be added — the 27th — was ratified in 1992, but it was actually proposed by Congress in 1789.