Angus King is trying to do something that Olympia Snowe could not do.

Sen. Snowe, a Republican, tried to strike a moderate balance between the highly disciplined members of her own party and Democrats who had become almost as partisan. Frustrated by her lack of success, she decided to retire from the Senate.

King, the former governor who is running as an independent, hopes to use his non-party status as a way of inducing the two major parties in the U.S. Senate to find reasonable common ground on key issues.

That’s unlikely to happen as the result of his being the senator in the middle, wielding the critical balancing vote in the Senate.

His opportunity to play that role depends on the outcome of as many as eight other Senate races considered right now to be toss-ups.

The results would have to be 50-49 either way for King to be the decisive vote. If so, he might be able to influence which party runs the Senate.

If he joined the caucus with 50 votes, it would have the majority needed to run the Senate. He could be rewarded with assignments to major committees.

If he joined the caucus with 49 votes, he could deny the other party control, forcing a compromise in Senate management and giving considerable power to the vice president who votes in the Senate when the parties are deadlocked.

At the moment, however, both parties are counting him in the Democratic camp, and thus not able to play this balancing game.

Would it make any difference to the Democrats if King went with the GOP, giving them control? The Democrats would still have enough votes to filibuster bills, blocking passage by a Republican majority. That’s just what the GOP has done recently.

Under Senate rules, a simple majority could eliminate the filibuster at the beginning of the session. The GOP is unlikely to do that, though the Senate Democratic leadership seems tempted.

King does not like the filibuster, but does not call for its outright repeal. He suggests the possibility of lowering the number of votes required to halt debate and force a vote from 60 to 55. That would certainly be favored by many Senate Democrats.

King would not even get the chance to play the “swing” role if the election produced a Senate with something like the current 53-47 Democratic majority, which includes two independents.

If the GOP held such a majority, it is not likely to back off conservative positions that it could see as having been approved by the voters.

The party breakdown of the close races is more likely to determine the balance than does King’s independent candidacy. A 50-49-1 outcome is only one of many possible results and is probably not the most likely.

The focus is on the Senate, because it is generally considered unlikely that the Republicans will lose their majority in the House of Representatives.

The real swing vote, if there is any, is in the White House. That’s especially true if the current split in control of the House and Senate continues.

With Mitt Romney as president, the only roadblock to Republican policy on health care, taxation and the budget would be Senate Democrats. If the GOP picks up five of the eight toss-ups plus the presidency, the Republicans could be in full control — except for the filibuster.

With Barack Obama as president and the current congressional divide, it is possible that the future would look much like the present. When announcing her retirement, Snowe indicated that she did not expect much change, and she could be proved right.

If Obama faced a solidly Republican Congress, it probably would yield the same result. The GOP would not have the two-thirds control of either house needed to override a presidential veto.

But all of these electoral calculations are likely to be beside the point.

If Washington is to begin producing results on taxes and spending, on measures that promote job growth and on health care, the swing that has to take place is in the minds of the people in Congress.

Once the elections are behind us, Snowe’s forecast needs to be proved wrong. The president, whoever he is, and party leaders would have to be willing to depart from the strict party line to find compromise.

Snowe was unable to get the Republicans to accept moderate compromises. King could have a better chance of influencing the Democrats to see his election as a message to adopt a moderate approach and produce at least some results on critical issues.