The move to defund Obamacare has been slow to gather support in the Senate. Really slow.

Republican Sen. Mike Lee has asked colleagues to sign a letter promising to "not support any continuing resolution or appropriations legislation that funds further implementation or enforcement of Obamacare." Of the Senate's 46 Republicans, just 12 signed the letter when it was released in late July.

In the weeks since, one more Republican, Sen. Mike Crapo, has joined the pledge, bringing the grand total to 13. That means 33 GOP senators have declined to sign.

The non-signers include some of the most conservative members of the Senate. This week I asked two of them — both determined opponents of Obamacare — why they have not joined the defunding effort.

"I'm not sure it's the best viable way at this point," said Alabama Sen. Jeff Sessions. "I've looked at it really hard, I've talked to Mike, and I certainly respect what he's doing, but I'm not convinced right now that this is going to be a way that will be successful and effective."

The Democratic-controlled Senate won't pass a defunding measure, Sessions argued, and the Democratic president would veto it anyway. "You end up in a government shutdown," he said. "There's no way to avoid this."

Wisconsin's Ron Johnson, who ran for the Senate on a promise to stop Obamacare, echoed Sessions' words. "I've done a lot of strategic planning in my lifetime, and the first step in developing a strategy is you have to recognize reality," Johnson said. "And it is a very sad, unfortunate fact that with President Obama in the White House, and Harry Reid in the Senate, the only way you can realistically defund Obamacare is to repeal it, and ... we haven't had one Democrat break ranks and join us."

Sessions and Johnson were careful to express their respect for Lee, and also to stress that they agree on the overall goal of stopping Obamacare. But the fact is, Republicans on Capitol Hill seem to be increasingly talking past each other on the subject. One group says, "We can't win," while the other says, "We've got to try."

Now some Republicans are laying out the math. Stopping Obamacare funding would require a Republican filibuster. That would take 41 votes to uphold. There are 46 Republicans in the Senate. That means that if just six GOP lawmakers broke ranks and voted with Democrats to continue funding, the effort would fail.

Several Republicans have already voiced outright opposition to the defunding proposal. Sen. Tom Coburn called it "dishonest." Sen. Richard Burr called it "the dumbest idea I've ever heard of." Sen. Roy Blunt said it "won't work." Sen. Saxby Chambliss said the same. So did Sen. Mike Johanns. Sen. Susan Collins said it's unrealistic. Sen. John McCain said it's not going to happen. Sen. Bob Corker called it a "silly effort."

That's eight who have chosen to speak out. None will vote for a Obamacare defunding measure that could lead to a shutdown. And if just those eight decline to support a defunding effort, it will fail. And remember, a total of 33 Republicans have declined to sign the Lee letter.

Faced with that reality, some Republicans are discussing a measure that would delay the arrival of Obamacare for a year, or at least delay the start of the individual mandate for a year (as President Obama did unilaterally with the employer mandate). In this scenario, a delay bill would be considered separately from a government funding bill, so there would be no shutdown threat.

The House has already passed a bill to postpone the individual mandate; 22 Democrats supported it. In the Senate, maybe one or two Democrats would go along. The problem, of course, is that even with a defection or two, Democrats have plenty of votes to filibuster the move, stopping it cold.

But maybe there's deal that could be made. Some Republicans are exploring the possibility of trading some of the changes Democrats want in the sequestration spending cuts in exchange for an Obamacare delay. But of course Republicans would be divided on that too; the sequestration cuts are the only real spending reductions the GOP has been able to force on the Obama administration. Would Republicans give even some of those up?

More than ever, GOP leaders fear the situation could lead to serious intra-party conflict. "We need to make sure that we're not shooting each other," said Johnson, "that we're not eating our own."

Byron York, the Washington Examiner 's chief political correspondent, can be contacted at byork@washingtonexaminer.com. His column appears on Tuesday and Friday on washingtonexaminer.com.