House Democrats are blaming Sen. John McCain (R-Ariz.) for scuttling an immigration package that was building support, though Republicans dismissed the story as a “fairy tale.”

A week before the March recess, House Democrats thought they were close to getting a deal on an immigration package that would include temporary visas for most illegal immigrants, expanded visas for temporary workers and border enforcement provisions.

Rep. Bart Stupak (D-Mich.), who was negotiating the package among disparate groups of Democrats and Republicans along with Rep. Rahm Emanuel (D-Ill.), said a senior Republican came to him and Emanuel and told them that McCain, the presumptive Republican presidential nominee, didn’t want to deal with immigration this year.

Stupak said at that point, momentum for the bill among Republicans stalled.

“McCain just felt it would be uncomfortable for him to have it hanging out there,” Stupak said.

Supporters thought they had about 200 to 205 Members for the package, including about 15 Republicans. They were targeting another 15 to 20 Republicans to put the bill over the top when the deal fell apart.

An Emanuel aide confirmed Stupak’s account that a senior Republican — not one of the top leaders — told them that McCain did not want to deal with the issue.

Immigration, however, was a hard sell in both chambers. Senate Majority Leader Harry Reid (Nev.) has said the issue would not go anywhere this year, and House leaders were equally skittish.

A House Democratic aide with knowledge of the negotiations blamed McCain.

“McCain is a one-man roadblock,” the aide said. “We were moving in the right direction before John McCain intervened and did what he could to slow this process down.”

Republicans dismissed the account from Democrats.

“They are peddling a fairy tale in an effort to blame Republicans for Democrats’ embarrassing inability to get anything done on immigration — a failure that is the result of two things: their unwillingness to work in a bipartisan way, and divisions in their own Caucus,” said Michael Steel, spokesman for House Minority Leader John Boehner (R-Ohio).

Steel added: “What put the kibosh on the Democrats’ plan to bring this bill up was Republican leaders saying the amnesty provisions will not fly with our Caucus.”

A call to McCain’s presidential campaign was not returned before press time Wednesday.

Stupak has been playing a key role in the immigration issue, having sponsored a bill extending the H2B visa program important to the local tourist industry in Michigan, while also being a co-sponsor of the border enforcement bill sponsored by Rep. Heath Shuler (D-N.C.).

Stupak said that the White House was aware of and was encouraging the bipartisan negotiations before they were told about McCain’s opposition. Stupak and other Democrats still hold out a slim hope of getting a deal on an immigration package, but the odds appear to be shrinking.

Republicans have launched discharge petitions on Shuler’s and Stupak’s bills, arguing both have majority support in the House but are being held hostage by Democratic leaders who don’t want to anger the Hispanic Caucus.

Hispanic Caucus members said they had not heard of McCain’s involvement one way or the other, but Rep. Luis Gutierrez (D-Ill.) said McCain’s recent backtracking from his support of comprehensive immigration legislation in favor of border security first has been “most unhelpful.”

“I know where his heart is at, but I don’t think he has the political will to do what his heart wants to do,” Gutierrez said of McCain, adding that he thought the backdrop of the presidential race wasn’t useful in getting a deal.

“We have over 80 percent of Democrats, but we can’t get 20 percent of the Republican Caucus to join us,” he said. “On a good day, 10 percent will join us. … There’s no movement from that side.”

Hispanic Caucus Chairman Joe Baca (D-Calif.) blamed GOP leaders, not McCain, for supporting discharge petitions rather than working with Democrats on a larger deal.

“Instead of working for something, they are trying to use it as a political wedge issue,” Baca said. “We were so close. We’re not giving up.”

The sticking point for Republicans and some conservative Democrats continues to be the Hispanic Caucus’ insistence that any immigration package provide at least temporary visas for illegal immigrants who have not committed crimes and pay back-taxes and fines. Baca argues that the package under discussion is not amnesty, although many GOP lawmakers say that anything that doesn’t force illegal immigrants to leave the country is amnesty.

“Whatever we do, nothing will lead toward amnesty, but it will take care of the 12 to 14 million with a temporary visa,” Baca said. “We’ve got to ignore the Lou Dobbs of the world.”