WASHINGTON – House Speaker Paul Ryan tried again this week to discourage speculation that he might be a compromise presidential choice at the coming Republican National Convention in Cleveland in July.

He echoed the famous rejection of Gen. William Tecumseh Sherman, who told Republican suitors in 1884, “I will not accept if nominated and will not serve if elected.”

In his own statement, Ryan put a fine point on it: “I should not be considered. Period. End of story.”

Ryan, who in 2012 was perfectly willing to run as the vice-presidential nominee with Mitt Romney, said that as co-chairman of the 2016 convention he would seek a rule restricting candidates to those who ran in the primaries.

Donald Trump’s new convention manager, Paul Manafort, quickly insisted that a Ryan candidacy would never happen because his man would be nominated on the first ballot, as he will go in with the 1,237 delegates needed.

But because Ryan also dismissed the notion that he would become House speaker before agreeing to fill that role, the chatter of his availability is likely to linger.

In a party depleted of credible alternative candidates, the establishment’s desperate search for a savior will go on.

Flat statements of unavailability for the highest offices have on occasion not held up. Most notably, President Theodore Roosevelt, who had announced in 1912 he would not run again, changed his mind in 1916 and launched a losing campaign against his chosen successor, President William Howard Taft, leading to the election of Democratic nominee Woodrow Wilson.

At the dawn of the Republic, the nation’s second vice president, Thomas Jefferson, decrying the prospect of emerging party factions, famously declared, “If I could not go to heaven but with a party, I would not go at all.”

Two centuries later, historian Arthur M. Schlesinger Jr. was moved to note: “The quadrennial presidential contest served, after Washington’s retirement, as an inescapable focus for national party competition and as a powerful incentive for national party organization.

Even Jefferson soon decided that, with the right party, he would be willing to go, if not to heaven, at least to the White House.” He formed the anti-Federalist Democratic-Republican Party and rode it into the Oval Office in 1800.

More often, presidential hopefuls have declared their unavailability for the vice presidency as if it were beneath them, only to accept when the top prize went elsewhere.

In 1980, when George H.W. Bush was losing his challenge to Ronald Reagan for the Republican presidential nomination, he often was asked by reporters whether he was persevering in hope of being the vice-presidential nominee.

He steadfastly and with some disdain would ever-so-cleverly answer: “Take Sherman and cube it,” referring to the old Civil War general’s disavowal of presidential ambition.

But after Reagan was nominated, and briefly flirted with taking on former President Gerald Ford as his running mate, the senior Bush eagerly grabbed the offer, putting himself on the path to the Oval Office eight years later.

Earlier this year, a cocky Gov. Scott Walker of Wisconsin, wrongly anticipating his own presidential nomination, floated the notion that he would take fellow presidential candidate Sen. Marco Rubio of Florida as his running mate. His equally cocky target replied that a ticket with Walker might not be a bad idea, but the other way around – Rubio for president, Walker for veep, a pipedream either way.

Currently, frontrunners Trump and Cruz, in a tough fight for the top spot on the GOP ticket, are keeping their own counsel on a running mate. As for Walker, who has endorsed Cruz after his early nosedive in the presidential race, he has said speculation that Trump might choose him was “almost breathtaking” and he’s “just happy being governor.”

Rubio, meanwhile, hasn’t endorsed anyone and is holding onto the 171 delegates he won in the early primaries, possibly as bargaining chips to salvage something from his once-hopeful campaign.

At last word, no present-day Sherman-like statement about the presidency or vice presidency has been heard from anybody else, beyond the well-courted Paul Ryan, who may already regret saying “yes” to becoming speaker of the House, given the gloomy GOP outlook.

Editor’s note: Jules Witcover’s latest book is “The American Vice Presidency: From Irrelevance to Power,” published by Smithsonian Books. You can respond to this column at juleswitcover@comcast.net.)