Rep. Barney Frank (D-Mass.) figures the nation could raise a little cash by licensing Internet gambling. Rep. John Conyers Jr. (D-Mich.) wants to save money on prison beds by letting convicts out early if they learn to read.

And House Armed Services Committee Chairman Howard P. “Buck” McKeon (R-Calif.) joined forces with Democrats on his panel to tell congressional budget-cutters where they should NOT look for savings: The Pentagon, which is already struggling to respond to two previous rounds of cuts.

This week, guidance from senior lawmakers poured into the offices of members of a special congressional panel known as the Joint Select Committee on Deficit Reduction. Friday was the deadline for submitting recommendations to the committee, which is under orders to identify at least $1.2 trillion in 10-year savings by Nov. 23.

It’s unclear how much the avalanche of advice will help the “supercommittee.” The Armed Services submission was one of several displays of bipartisan unity. Senate budget leaders teamed up to call for a two-year, rather than annual, budget process. And congressional agriculture leaders in both chambers were expected to offer to slice $23 billion from federal farm programs, a significant sacrifice that could mean the end of direct payments to farmers.

Still, most lawmakers stayed within well-worn policy grooves, with Democrats calling for higher taxes and more economic stimulus to tame the rising national debt and Republicans calling for cuts to the health and retirement programs that are projected to be the primary drivers of future borrowing.

By all accounts, that ideological divide, which torpedoed hopes for compromise during the debt-limit debate this summer, continues to bedevil the 12 supercommittee members. Republicans are open to some modest tax increases by ending subsidies for oil and gas companies and corporate jet owners, for example, but have so far resisted the more substantial tax increases that Democrats are demanding in exchange for cuts to federal health programs, according to aides and lawmakers with knowledge of the deliberations.

No one has given up hope, but no one can quite make out the path forward, either.

“Whether we are able to overcome some of the obstacles by the end of the day is still unclear,” Rep. Chris Van Hollen (D-Md.), a supercommittee member, said Friday at an event sponsored by the National Journal.

Top administration officials, meanwhile, reported Friday that the nation recorded a $1.3 trillion budget deficit in the fiscal year that ended last month, the third straight year of deficits in excess of $1 trillion. The figure was a bit better than President Obama predicted in February, with the recovering economy lifting tax collections and pushing down federal safety-net spending. But it nonetheless swelled the national debt, which on Friday stood at about $14.8 trillion.

With the clock ticking toward its Thanksgiving deadline, the supercommittee has been meeting daily behind closed doors to develop a framework that could include cuts to health programs and other mandatory initiatives such as federal worker pensions, as well as tax increases. The panel could also leave the question of taxes to the regular legislative committees, issuing instructions for them to undertake a rewrite of the code sometime next year. If the committee fails to reach its target, across-the-board cuts to defense and most domestic programs would be triggered in January 2013.

Given the magnitude of their task, perhaps committee members will eagerly scour their colleagues’ letters for any scrap of actual savings. If so, they might be tempted to act on Frank’s missive, in which the senior Democrat on the House Financial Services Committee also offered this nugget: Treasury Secretary Timothy F. Geithner routinely takes military air transport instead of flying commercial, costing taxpayers at least $150,000 a pop.

Alas, the savings were apparently illusory. After hearing from Treasury, Frank retracted his proposal.

“I have now gotten more information than I had before about the Treasury Secretary’s travel. I made the mistake of acting on inadequate information,” Frank said in a statement. “Based on the information I have now gotten — and that I should have looked into before — I now believe that the Secretary’s travel patterns are appropriate and do not need any mandated change from us.”