As Congress readies for a fall fight over appropriations and the Joint Committee on Deficit Reduction’s directive to find at least $1.2 trillion in spending cuts, Republicans could face a slew of unsolicited advice from the collection of armchair quarterbacks who make up the party’s presidential field.

Former Speaker Newt Gingrich (Ga.) addressed the conservative Heritage Foundation in August and bluntly urged Congressional Republicans to junk the committee created by enactment of the law that raised the U.S. debt limit just in time to stave off default. Days earlier, more than a half-dozen GOP presidential candidates  argued, during a debate in Iowa, that Congressional Republicans were wrong to agree to a debt ceiling increase under any circumstances.

Debate moderators pressed the candidates to stake out a position on whether they would accept tax increases if there were $10 cut from the deficit for every dollar offered of a tax increase. All contenders said they would oppose such a deal.

With at least three presidential debates scheduled for this month alone and two fall deadlines for Congressional action on the horizon, House and Senate Republicans are likely to get an earful of unwanted — and in some cases, politically unhelpful — advice from the GOP’s White House field. How this intraparty dynamic affects Republicans on Capitol Hill remains an open, and potentially important, question as Congress gets back to work after its five-week summer recess.

One Republican operative who worked for a 2008 candidate said the GOP hopefuls would be better off ignoring Congress and focusing on President Barack Obama. But this operative, who is currently unaffiliated, said the Republican White House contenders are likely to get drawn into the fight on Capitol Hill given the intense media scrutiny expected to descend on the bipartisan, bicameral deficit panel and the debate over fiscal 2012 spending.

“Smart politics would be for GOP candidates to keep the focus on Obama, not Congress. Obama is running against Congress right now because he doesn’t have an actual opponent,” the operative said. “Where candidates may get tripped up in the coming months is responding to Congressional actions like the super committee’s recommendations or another [continuing resolution] that the media wants comment on. 

“There’s little to be gained by getting into the weeds of legislation,” the operative added. “Best to stick with executive-level leadership.”

Congress faces a Sept. 30 deadline to agree on fiscal 2012 appropriations and avoid a government shutdown. The joint committee has been given a Thanksgiving deadline to agree on a wide-ranging deal on deficit reduction to prevent an automatic trigger from taking a huge slice out of defense spending, Medicare providers and numerous government programs.

Democrats on the committee are expected to demand tax increases in exchange for agreeing to sizable spending cuts, which — as during the summer fight to raise the debt ceiling — will be a no-go for the Republicans on the panel. How that key difference is bridged remains unclear at the outset of the committee’s negotiations.

Obama might offer his own recommendations to the panel, which could include proposals for spending cuts and revenue increases greater than the $1.2 billion in deficit reduction required to allow for the next debt ceiling increase needed to get the U.S. through the presidential election.

Republicans in the House and Senate could get an earful from the GOP White House candidates looking to position themselves with primary voters dissatisfied with Congress’ performance. Polls have shown Republican and conservative voters to be equally unhappy with the GOP-controlled House and the party’s minority Conference in the Democratic-run Senate.

Former Massachusetts Gov. Mitt Romney was criticized by his 2012 rivals for avoiding taking a position on the debt ceiling increase plan. Ultimately, he opposed the deal that Obama struck with Speaker John Boehner (R-Ohio).

But one senior Republican Senate aide disputed the notion that Congressional Republicans would pay much attention to anything the GOP presidential candidates have to say.

This aide also questioned how involved the presidential field might become in Capitol Hill politics, given how unpopular Washington — and its politicians — is with the public.

“I don’t suspect the presidential candidates would spend their time giving anyone advice on the debt committee nor do I think it would be effective if they did,” the senior Republican Senate aide said. “Their job requires them to be as far away from the Beltway, politically and literally, as they can. Once we have a nominee, that calculus will change.”

And yet the current GOP field lends itself to exactly that kind of intervention.

Of the Republican candidates, two are House Members with substantial followings, and Gingrich is a former Speaker who has focused much of his campaign rhetoric and proposals on what Congress should do to address various problems. Rep. Michele Bachmann (Minn.), a frontrunner, has campaigned on her August vote against raising the debt ceiling. She ran ads on the issue in Iowa and will likely use her opposition as a stump line throughout the campaign. Rep. Ron Paul (Texas) is a regular critic of the House GOP.

Other Republicans running are former Sen. Rick Santorum (Pa.), Rep. Thaddeus McCotter (Mich.) and Texas Gov. Rick Perry.