WASHINGTON, July 13 — With the Senate stymied so far in its bid to assemble enough votes to sway the White House on Iraq, two leading Republicans offered a new approach on Friday that would require President Bush to present a strategy by October that began limiting the involvement of American forces.

There are, it seems, nearly as many Iraq proposals circulating on Capitol Hill as there are senators who question the war. And so far, none of the attempts to change course have succeeded in transforming a dissent that is palpable among Democrats and Republicans into a wide enough majority to withstand a filibuster or a presidential veto.

In offering the proposal on Friday, Senators John W. Warner of Virginia and Richard G. Lugar of Indiana were seeking to reach that elusive goal when the Senate resumes its debate next week. The two senators, among the most respected Republican voices of military and foreign policy, are seeking to attract Democrats as well to the plan, which also urges Mr. Bush to seek a new war authorization from Congress in September.

But despite the irrefutable sour public opinion on the war, there remains deep discord in Congress over the politics — and substance — of proposals presented during a protracted six-month Iraq debate in Congress. Lawmakers say the fact that Iraq has become a central issue in a spirited presidential campaign has also emerged as an obstacle to the kind of bipartisan accord that Mr. Warner and Mr. Lugar say they are seeking.