House Budget Committee Republicans emerged from a private meeting with Majority Leader Eric Cantor (R-Va.) today no closer to resolving their internal fissures over the size of the 2013 budget.

Cantor and Budget Chairman Paul Ryan (R-Wis.) discussed several paths forward with the group — most of which involve lowering the fiscal year 2013 spending cap below July’s Budget Control Act number of $1.047 trillion.

But Members are still sharply divided heading into a weeklong recess about exactly where to set the mark, and with just weeks to go before their self-imposed deadline to produce a budget, the fate of the blueprint hangs in the balance.

Still, Cantor said after the meeting that the talks are “on track” and noted that he thinks the committee can pass a spending plan before month’s end.

“I’m looking forward to seeing the markup occur on schedule and a budget on the floor by the end of this month,” the Virginia Republican told reporters.

Ryan echoed Cantor’s optimism, adding that he will release a plan the week after next, when the House comes back from recess.

“We’re waiting for a baseline to finalize our budget, so obviously our budget’s not finalized because we don’t have a baseline,” the Wisconsin Republican said. “But we’re on track with where we wanted to be, and we’re on schedule with when we want to bring our bill up.”

Meanwhile, Speaker John Boehner told reporters Thursday morning that he is awaiting word from the committee.

“We’re working with our Members through the normal legislative process to develop our budget,” the Ohio Republican said. “Our Members are having a discussion about what the budget should look like. I’m waiting for the outcome of those conversations.”

Staff will work throughout the recess week to craft a bill to which Republicans on all sides can agree. But with hard-line conservatives insisting on deep spending cuts and appropriators pushing for a high spending ceiling, the road forward might be impassable.

“It’s not easy, obviously. There are differences of opinion within our Conference,” said Rep. Mike Simpson (R-Idaho), a member of the Budget and Appropriations committees.

Simpson and his fellow appropriators want to keep the budget in line with the BCA because it would make it easier for them to pass their spending bills with bipartisan support. But fervent pushback from the conservative Republican Study Committee has made that number impossible.

Among the proposals discussed in the private meeting was a plan to set the mark at $1.028 trillion, in line with last year’s Ryan budget. But Budget Committee Vice Chairman Scott Garrett (R-N.J.), who with his fellow RSC members has pushed to set the mark lower, said the number “is still problematic.”

“It has been concern for me and a number of others as well,” he said.

Another concern for the group is how long it takes to balance the budget. The proposal Members were presented with Thursday would do so in about 29 years, Members said, but the RSC wants the plan to balance much sooner.

Ryan and Cantor also outlined for the first time how they hope to deal with the sequestration process that will force Congress to cut $97 billion in discretionary spending and $13 billion in mandatory spending in fiscal 2013.

The committee could pass a reconciliation bill, they noted, instructing committees of jurisdiction to find those savings above and beyond the budget baseline. One option could be reassigning about $70 billion in those discretionary spending cuts to the mandatory side of the ledger through the reconciliation process.

The two leaders sent a joint memo to all Member offices Thursday with a “budget reconciliation primer” outlining in general terms of what the process is and how it works.

But asked whether such a move would be included in his plan, Ryan said only, “You’ll see when we release our budget.”

Regardless, RSC members are already grousing about the proposal.

The group’s chairman, Rep. Jim Jordan (Ohio), said Thursday that any cuts to mandatory spending should come in addition to the discretionary cuts called for in the sequester, not in lieu of them.

“Of course we should try to achieve savings in the mandatory spending,” he said. “We think that’s good. But we would prefer that be in addition to the way the law reads.”

Meanwhile, the internal strife in the House GOP has caught the eye of Democratic Senators who plan to stick with the BCA in writing their spending bills.

Democratic Senatorial Campaign Committee Chairwoman Patty Murray (Wash.) blasted the House GOP in an interview Thursday and said its plans to deviate from the BCA is “setting the stage for a government shutdown.”

The two sides could still be arguing about spending levels right up to the Sept. 30 deadline, when the law that funds the government expires, making for yet another high-stakes showdown.

“They are showing us once again that a deal is not a deal, and that is very dangerous moving forward,” Murray said. “If they insist on breaking the deal … then they are setting the framework for us not being able to do our jobs.”

Jessica Brady contributed to this report.