One of Washington’s favorite parlor games is conjecturing about the remote possibility of an Electoral College tie. Prognosticators have come up with various maps and scenarios under which the election would result in a 269-269 deadlock, which would vest the responsibility of choosing the country’s leaders squarely in what polls say is one of the least popular institutions in the country — Congress.

There’s little dispute about what would happen in the main event. Next year’s House would choose the president, with each state delegation casting one vote. Unless an unanticipated tidal wave arises Nov. 6 on behalf of Democrats in House races, Republican Mitt Romney stands to win, largely because the system would work to the advantage of smaller, rural states.

One question that has been debated in the past, whether some Members would feel pressure to ignore their own party and vote for the winner of the popular vote in their state, seems to have faded as the result of gerrymandering and rising partisanship.

“That kind of extreme partisan polarization seems to rule over everything,” said Richard Arenberg, who worked on Capitol Hill for more than 34 years, including for former Senate Majority Leader George Mitchell (D-Maine). “So many of these Members of the House have safe seats.”

“The Republicans have shown incredible discipline within their caucuses,” added former Sen. Ted Kaufman (D-Del.), who spent decades working in the Senate for Vice President Joseph Biden.

The outcome might be less clear in the Senate, which in the event of a tie would be charged with picking the vice president, with each Senator in the 113th Congress casting one vote.

One of the foremost experts on Senate rules said he sees no evidence of expedited procedures to avert a filibuster of that process.

“I have read the 12th Amendment to the Constitution, and I don’t see anything that requires the Senate to vote without debate on choosing a vice president,” former Senate Parliamentarian Robert B. Dove said. “Therefore, I don’t see what would stop Senators from speaking about who is going to be the vice president and, in effect, forcing a cloture vote.”

While the parliamentarian advises the presiding officer on procedural questions, Dove said, the responsibility to rule rests with the occupant of the chair. In the event of an Electoral College tie, that would be Biden (in his capacity of president of the Senate, until Jan. 20). Dove notes that Democratic Vice President Hubert H. Humphrey disregarded the parliamentarian’s guidance with some regularity.

Kaufman said that while all these arcane procedural options exist, cooler heads should prevail.

“The mood of the American people would be very powerful,” Kaufman said. “I don’t think Congress is in a strong enough position” to go away from the electorate. Kaufman suggested that there might be pressure on the Senate to follow the popular vote, regardless of the Electoral College tally.

Another option would be to acquiesce and appoint the running mate of the president selected by the House. One precedent might be the 2000 election, when Democrat Al Gore accepted the ruling of the Supreme Court in the disputed Florida election results in the interest of national unity.

“In general, party unity within the White House makes sense. But there is no requirement, and we’ve had presidents of one party serve with [vice presidents] of the other,” said Vikram David Amar of the law school at the University of California, Davis. He has written about the history of the Electoral College.

Things could get rough if the Senate is tied 50-50. Based on the amendment’s requirement for a majority of Senators, Dove said he thinks that the vice president could not break a tie.

The 12th Amendment was ratified four years after the infamous 1800 election, in which the House broke a tie between Thomas Jefferson and Aaron Burr, picking Jefferson on the 36th ballot. The House chose John Quincy Adams over Andrew Jackson in 1824, but John C. Calhoun won the Electoral College vote for vice president. The only time the Senate selected the vice president was after the 1836 election, when several state ballots had different running mates for Martin Van Buren. It chose Richard M. Johnson, a Kentucky Democrat.