DUBLIN, N.H. — Senate Republicans who advocate defunding Obamacare admit they don't have the votes to make it happen and are having trouble convincing fellow GOP lawmakers — much less any Democrats — to join their cause. With an end-of-September deadline approaching, their last remaining option is to somehow persuade millions of ordinary Americans to become activists on behalf of the proposal. Those millions would rise up and put pressure on lawmakers, who would then be forced to join the defunding drive. It's a pretty far-fetched victory scenario.

But it's all they've got. "I have been traveling all over the country working to energize the grassroots and mobilize the American people to rise up and to stop Obamacare, to defund Obamacare," Republican Sen. Ted Cruz told reporters here in New Hampshire Friday shortly after arriving for his first-ever appearance in the nation's first-primary state. "The only way we're going to succeed in defunding Obamacare is if it comes from the American people."

"This is not a strategy of trying to convince Washington, D.C.," Cruz declared. "It's a strategy of empowering the American people."

Translation: The defunders don't have anywhere near enough votes to succeed. At the moment, they have 14 out of 46 Republicans in the Senate and 80 out of 233 Republicans in the House. (And no Democrats in either chamber.) Looking at both bodies as a whole, the defunders have the support of 14 percent of the Senate and slightly less than 19 percent of the House. Cruz and his allies know that won't work.

So they have embraced the grassroots revolution scenario. They have started a website, Dontfundit.com, and are asking people to visit the site and sign an online petition for defunding. By mid-day Monday, the site had about 575,000 signatures. As online petitions go, that's a pretty good number, but it's not earth-shaking. (In comparison, a MoveOn.org petition demanding that Macy's stop selling Donald Trump's clothing brand has 689,000 signatures.)

A major disappointment for the defunding advocates has been their failure to recruit some of the Senate's most conservative members. In New Hampshire, I asked Cruz why he had not been able to convince colleagues like Jeff Sessions and Ron Johnson — certainly not RINOs, not captives of the Washington establishment — to join the movement.

"The momentum is moving in the right direction," Cruz answered, noting that the 80 signers in the House include a number of new additions, and one Republican senator has joined in the last week. But those numbers will grow only by creating a wave of public opinion, he said, a development that will not only bring more Republican lawmakers on board, but some Democrats, too. "If you're a Democrat, particularly in a red state, who's up for election in 2014, and you start to hear from 5,000, and then 10,000, and then 20,000, and then 50,000 of your constituents, suddenly the calculus starts to seem very, very different," Cruz said.

The problem, of course, is there's no evidence that such a wave of public opinion is forming. Short of winning overwhelming support, the defunding plan involves the possibility of temporarily shutting down the government, or part of the government, unless Barack Obama agrees to abandon the signature initiative of his presidency. But a new survey done for Republican members of Congress by GOP pollster David Winston found strong opposition to a shutdown not just among Democrats and independents, but among Republicans, too.

In Winston's poll, 71 percent of those surveyed said they opposed a shutdown, versus 23 percent who favored one. Among Republicans, 53 percent opposed a shutdown, while 37 favored one.

In the absence, so far, of a groundswell, the defunding movement is nevertheless succeeding in creating tensions between Republican lawmakers. New Hampshire Republican Sen. Kelly Ayotte, who has not signed on to the defunding movement, introduced Cruz on Friday. As senators do, both she and Cruz spoke highly of each other. "He has passion, he has principle, and he is very smart," Ayotte said of Cruz, who in turn praised Ayotte as "a rock star" and "tough as granite."

But behind all the niceties lies a serious disagreement on Obamacare. As Cruz outlined his plan to create a "tsunami" of public opinion — a proposal that drew plenty of applause from the Republican activists in the crowd — Ayotte stood not far away, not joining in.

The moment highlighted a nettlesome problem for Republicans. They're united in opposing Obamacare but find themselves consumed by internal squabbles over how to proceed. Could President Obama and his Democrats wish for anything more?