When Massachusetts voters choose a governor on November 5, they’re more likely to be thinking about, say, tolls on the Turnpike than the balance of power in Washington, DC. But they might want to pause a moment to consider the question of party labels and power politics on the national level. After all, if Mitt Romney is elected governor, he will continue a 12-year tradition of this most-Democratic state maintaining one top official who is welcome among power Republicans in the nation’s capital. If Shannon O’Brien wins, on the other hand, our state will present a united– that’s to say, all-Democratic– front to federal officeholders. At a time when Republicans occupy the White House and control of both houses of Congress is teetering on a razor’s edge, it makes sense to ask: Does it matter in DC whether the State House corner office is occupied by a Democrat or a Republican?

It’s not an easy question to answer. Our state’s political oomph in Washington has been in flux since at least the mid-1990s. In the 1970s Boston enjoyed the nirvana of having a local boy, Tip O’Neill, rise to Speaker of the House in a Congress overwhelmingly dominated by liberal Democrats favorably inclined toward the Northeast. With the help of titans like Ted Kennedy and the late Joe Moakley, O’Neill took good care of the Bay State, securing billions of federal dollars for Massachusetts projects and otherwise looking out for the Commonwealth’s interests.

O’Neill’s retirement in 1986 may have signaled the beginning of the end of federal largesse for Massachusetts, but the party was really over in 1994, when Republicans seized control of both houses of Congress for the first time in 40 years. At first, the state’s two GOP congressmen, Peter Blute and Peter Torkildsen, helped keep the lines of communication open with the new lords of the House, but in 1996 Massachusetts voters threw the state’s only emissaries to the national Republicans out of office. “Massachusetts is now a caricature of itself in Washington,” Blute groused after his loss. “It’s not a good thing to be a one-party state…You have to have a voice in each cloakroom and in each meeting.”

But even in the darkest days of the Gingrich revolution, the state’s solidly Democratic delegation still had a direct line to the Clinton White House. So much so, in fact, that The Boston Globe reported that the state’s 10 representatives in the House thought of Clinton as “the 11th member” of their team.

The state has used its rare Republican officeholders to good advantage.

After the 2000 election, however, that gig was up. But a new source of Bay State influence in Washington arose: Gov. Paul Cellucci. Not only was Cellucci a member of the president’s party, he had longstanding ties to the Bush family and was tight with White House Chief of Staff Andy Card from their days as state legislators. Cellucci quickly cashed in on that connection himself, scoring an ambassadorship, but his acting-governor successor, Jane Swift, could at least count on party ties to keep up the good will. Then the congressional tables got turned again, at least in part. Thanks to Jim Jeffords’s epiphany last spring, Democrats retook control of the US Senate, which restored immense influence to the state’s senators — John Kerry and, in particular, Ted Kennedy.

Thus, despite the overwhelmingly Democratic character of the Massachusetts political establishment, the state has used its rare Republican officeholders– and the shifting sands of congressional politics– to good advantage in Washington. The question is: What’s at stake today in preserving, versus severing, the state’s last bond with the GOP?

This question comes at a precarious moment for the Commonwealth. State officials are keenly interested in several major issues on the Washington agenda for next year, including funding for new homeland security programs; reauthorization of the 1996 welfare reform law; likely adjustments to Medicare and Medicaid funding; and, above all, renewal of federal transportation legislation, which sets the formula for handing out road and transit dollars across the nation. Twenty years ago that transportation bill would have been a windfall for the Bay State. Now, rather than payout, it’s payback time. “The members get berated all the time,” laments one state official. “It’s, ‘You don’t need any more money. You already got billions of dollars.'”

There is a strong consensus among observers that a state is better off sending one senator from each party to Congress, says Stephen Hess of the Brookings Institution, a public-policy think tank in Washington. Bipartisan representation in the two-seats-per-state upper house guarantees one powerful emissary to the White House on matters like judgeships, federal grants, and legislation affecting state interests, no matter which party holds the presidency, he says. It’s less clear that the party affiliation of the top state official will affect the state’s reception in Washington, but Hess says that in the Bush White House, Romney might well get a warmer welcome than O’Brien would.

“The fact is, George W. Bush comes out of a state house and has been very supportive of Republican governors, and has even recently campaigned for some,” says Hess. “I rather suspect the chemistry would be good between Romney and Bush.”

Anne Gavin, who runs the state’s office of federal affairs in Washington for the Swift administration and has dealt extensively with the Bush White House, agrees. “I think it does help when you’ve got the governor having relationships at the White House, particularly in this administration, because so much of the cabinet are former governors,” says Gavin. “It’s sort of like a brotherhood.”

But– surprise, surprise– Democrats disagree. “We haven’t gotten the sense that people in the governor’s office have some kind of Bat Phone connecting them to the White House,” says an aide to one Massachusetts House member. What’s more, Democrats argue, the state’s best-placed ally in the Bush administration, Andy Card, shows few signs of holding their party affiliation against them.

Everyone seems to agree that the Card connection has been a boon for the state so far. For instance, Gavin says Card was instrumental last year in settling a dispute over federal labor regulations: A White House executive order required federal projects like the Big Dig to open bidding to non-union labor. State officials predicted the move would cause chaos and further budget overruns (not to mention political headaches in a union town like Boston). Those officials appealed directly to Card and won an exemption for projects, like the Big Dig, that were already underway. But it isn’t clear that it was the GOP governor who carried the day; Kennedy lobbied fiercely for the exemption as well.

And that kind of episode, when an issue turns on presidential directive, is the exception, not the rule, according to former Oklahoma Republican congressman Mickey Edwards, now at Harvard’s Kennedy School of Government. He says states get most of their federal goodies from the annual budgets and program funding formulas that are written in Congress.

“Most decisions affecting Massachusetts are made in the legislative branch,” Edwards says. “When there’s competition for funding and grants, sometimes the White House can dole it out. But most of the time there’s a formula, so the White House doesn’t have much influence.” The White House would be most likely to offer a state dramatic aid, he says, if a Republican official in a tight re-election race needed some good news to give to voters.

With Card returning Democrats’ phone calls and the real action taking place on Capitol Hill anyway, perhaps voters need not take into consideration what party their governor belongs to. After all, as majority-party members of the Senate, Kennedy and Kerry can do plenty of heavy lifting for the Commonwealth. But that will be true only if Democrats retain control of the Senate this fall. It would take just one more seat to fall into Republican hands for the GOP to reclaim the chamber. Then, assuming that the Republicans hold onto their House majority, the GOP would hit the coveted trifecta: control of the House, the Senate, and the White House. If that happens, it would probably take more than a Republican in the governor’s office to get Massachusetts out of the DC doghouse. On the other hand, should the Dems hold onto the Senate, and somehow take back the House…

Of course, this is where the head starts to spin. Game theory aside, the Commonwealth generally makes out best when its political emissaries– congressmen and governor– have solid support at home and a common agenda in Washington. For projects like the Big Dig and more modest pursuits, that’s held true for many years, through a variety of partisan combinations. Gov. O’Brien might play the Washington game differently than Gov. Romney, but with a congressional delegation that’s savvy and senior, even if lopsided, it’s hard to see either of them turning up losers.