Hold your breath — and feign a confident smile.

That pretty much sums up the mood among House Republicans as they brace for a potentially devastating special election result in Mississippi on Tuesday. A loss there would cloud any GOP efforts to shape the news this week, including the rollout Wednesday of a family-friendly agenda engineered by Texas Rep. Kay Granger and other women Republicans.

The Democrats might experience their own shortness of breath as they tackle legislation to fund military operations in Iraq and Afghanistan through the early part of 2009, but their hurdles remain more practical than political — and pale in comparison to the Republicans’, unless their wheels really come off.

The Republicans

The big question this week: Will a loss in Mississippi force House Republicans to make any major changes in their leadership or at the National Republican Congressional Committee? The answer so far has been a resounding no, and most lawmakers believe there is not enough time before the November election to do anything drastic.

In a last-minute frenzy to stave off disaster, Republicans are scrambling to hold the northern Mississippi seat with a series of phone banks, recorded get-out-the-vote calls from Arizona Sen. John McCain and first lady Laura Bush, and a visit Monday night by Vice President Cheney. But even a win comes with repercussions; the party’s cash-strapped campaign committee has already been forced to spend nearly $1.3 million defending a seat in the historically conservative district — a sizable sacrifice for an organization that still struggles to raise money.

Bad news from Mississippi would make it much harder for GOP leaders to build any buzz for the planned rollout of the family agenda Granger and others plan to introduce as the first plank of a long-awaited policy platform Republican leader John A. Boehner of Ohio promised early last year.

As part of this effort, Republicans will unveil a new slogan embracing the “change” motif that has dominated the presidential race: “Change You Deserve.” If the new slogan sounds familiar, it’s because it’s the same one that’s used for a drug widely marketed as an antidepressant.

The Democrats

Democrats should have plenty to cheer about if they steal another seat in the South. But those headlines won’t last if members of the majority fail to execute in Washington.

The Democrats’ major impediment is still the emergency supplemental to pay for the wars in Iraq and Afghanistan. A number of Blue Dog budget hawks are threatening to block consideration of that legislation because Democratic leaders failed to offset the cost of nearly $52 billion in expanded college aid for veterans over the next 10 years.

House Speaker Nancy Pelosi of California has had enough influence on Democratic members to override most of the previous internal objections to legislation on the House floor, and she has plenty of other bills with which she can mollify her fiscal conservatives this time around. These include a House-Senate compromise on the annual budget blueprint and the massive Farm Bill.

The Blue Dogs were angling for stricter protections against deficit spending in that budget document, so leaders might promise some offsets on future bills — like, say, an annual measure that tends to resurface every fall to shield taxpayers from the alternative minimum tax.

The Blue Dogs’ demands for the supplemental spending bill remain fairly vague; they say they object to the principle, not to increased money for veterans’ education, and Tennessee Rep. John Tanner said he’s working with Ways and Means Committee Chairman Charles B. Rangel. So Pelosi and her No. 2, Majority Leader Steny H. Hoyer of Maryland, should have enough wiggle room to work out a face-saving deal that would allow them to bring the war funding package to the floor.

Aides have had preliminary discussions about the possibility of allowing Blue Dogs to introduce a separate amendment requiring Congress to pay for the additional education funds. That could create extra complications for leaders, but the Senate could always just take it out.

Otherwise, Democratic leaders have structured the Iraq vote to minimize political pain for everyone. Opponents of the war can vote for an immediate phased withdrawal. Members can also approve funds for the war and oppose the domestic spending, or vice versa.

However, Democrats could endure some negative headlines if they suspend consideration of the package another week. And overall, the wrangling distracts from the No. 1 issue on their priority list: the economy.

To that end, expect more noise in support of a package the House approved last week that would create a federally insured safety net for borrowers and lenders who voluntarily agree to devalue home loans.

And, of course, what’s another week in Washington without more rhetoric about gas prices? Democrats are expected to introduce legislation in both the House and the Senate later this week that, in an effort to ease gas prices, would prevent President Bush from depositing oil into the Strategic Petroleum Reserve.

But will it be enough to insulate Congress from the political backlash brought on by surging oil prices? One very safe Republican worried last summer that if gas prices exceed $4 per gallon this summer, he would have to spend quite a bit of money defending his seat. At Washington-area gas stations, at least, that unhappy benchmark is now in the rearview mirror.