WASHINGTON (CNN) -- The Senate won't return to the debate over the troop increase in Iraq until getting back from a recess in two and a half weeks, Majority Leader Harry Reid said Thursday. But when it does, Senate Republican leaders say they will "insist" on getting votes on the same GOP resolutions that led to the current stand-off.

What remains unclear is if either side will have the votes at that time to break the stalemate.

Democrats got a boost Wednesday when seven Republican senators who oppose the troop increase but who voted with party leaders to block action on a resolution disagreeing with the "surge" issued a letter calling the stand-off "unacceptable."

Sen. Charles Schumer, D-N New York, Thursday called the letter a "mea culpa" on the part of the GOP senators, an acknowledgment that they made a "huge mistake" voting against the Democrats, he said.

One of those seven seemed to agree.

"I think we need to do honor to this institution and this country by debating and voting on the question," said Sen. Olympia Snowe, R-Maine. She said her vote Monday was aimed at spurring negotiations between Senate leaders not halting debate.

"We're barely a month into this session and we're already at a political detour, now returning to the partisanship of the past which was repudiated by the American people," she said.

Meanwhile, House Democratic leaders, hoping to avoid some of he same pitfalls that stymied Senate Democrats, announced the language of the resolution to be debated and voted on the House floor next week will be simple and straightforward: Congress supports the troops but opposes the president's plan.

Reid said Senate Democrats will offer language to the first bill on the floor when they return from recess, a bill implementing recommendations of the 9/11 commission. He said he hasn't decided if he'll offer the non-binding Levin-Warner resolution that got stuck this week or some other binding legislation. He might choose the House-passed bill, he said.

An aide later explained Reid is inclined to start with the Levin-Warner resolution.

The outcome of that action is unclear. While the majority of the Democrats may be joined by the seven Republicans who signed the letter, plus the only other known Republican supporter of the Levin-Warner resolution, Sen. Sam Brownback of Kansas, it could still leave that group a few votes shy of the 60 that will be needed for passage.