By ERICA WERNER 07/18/13 09:27 PM ET EDT AP

WASHINGTON — Supporters of far-reaching immigration legislation fear they're losing the message war and say an all-out campaign is needed from business groups and other outside advocates with ties to House Republicans to turn it around.

With House action now on hold until September at earliest, immigration bill backers see Congress' monthlong August recess as crucial to their cause. They're making plans to try to ensure that supporters of an immigration overhaul are heard as loudly as opponents when lawmakers return to their districts for town hall meetings and other events.

"Here's the fact: We're not winning, so we've got to wage a campaign," Sen. John McCain, R-Ariz., said Thursday. "There are many members of the House that don't want to take up any bill at all, as you know. What our job is, we want to convince them to at least pass legislation, so that we can go to conference and work together."

Immigration legislation, a top priority for President Barack Obama, has been in limbo since the Senate last month passed a sweeping bill with provisions aimed at securing the border, requiring employers to verify their workers' legal status, allowing many more workers into the country legally, and offering eventual citizenship to the 11 million immigrants already in the country illegally.

Many members of the House's Republican majority oppose citizenship for people who crossed the border illegally or overstayed their visas, and House Speaker John Boehner, R-Ohio, has ruled out taking up the Senate bill in the House. Instead, he's declared that the House will move in a piecemeal fashion with a series of individual bills, beginning with border security.

Although Boehner had hoped for House action on immigration before August, that goal is no longer in sight. He reiterated Thursday that the House must address the issue. When and how remained unclear, although Boehner said he hoped to see the House pass something on immigration before Congress next confronts raising the U.S. debt ceiling, which is expected to happen sometime this fall.

"The House is going to do its job, and we're going to do this in a commonsense, step-by-step way," Boehner said. "Because the American people have kind of had it with 1,300-page bills that no one's read."

Individual House Republicans are grappling with the issue. Particularly vexing is the question of the millions already here illegally. Some conservatives oppose any kind of legal status for them, but others are open to offering them legal guest worker status and perhaps more. Boehner this week endorsed citizenship for those brought to the U.S. illegally as children.

For now, Democrats are opposed to any solution that falls short of citizenship for all 11 million in the country illegally.

The debate promises to play out in August as business, religious, agriculture and other groups in favor of reform mount a campaign to promote it. On the other side, conservative tea party groups who tend to turn out in large numbers for town hall meetings will also be making themselves heard.

"August is a month in which either legislative proposals die, or they survive," said Sen. Robert Menendez, D-N.J., another author of the Senate bill. He said those who favor immigration legislation must be heard in August. "And if we do that, we'll be well positioned for the fall in the House. If we don't, then we run a risk."

McCain, Menendez, Sen. Chuck Schumer, D-N.Y., and other authors of the Senate bill summoned a large group of business lobbyists, officials with religious groups and others to the Capitol earlier this week to tell them they needed to work harder and coordinate better to win over individual House Republicans. The senators distributed a list of 121 House Republicans seen as persuadable on the issue and instructed those present to focus on tailoring individual campaigns for their congressional districts to win them over.

"We are going to have numerous business contacts – whether it be a local restaurant that cares about immigration or a high-tech or manufacturing or financial business in their district – contacting them in terms of how important this is to the future of jobs in each district," said Schumer. "The economic message is the message that business can best send and I think that will resonate best with undecided Republicans."

Kevin Appleby, director of migration and refugee policy for the U.S. Conference of Catholic Bishops, was among those attending the meeting.

"The key to victory is that all interested parties must work for the entire bill, not just their piece," Appleby said. "We all live or die together."

Neither Schumer nor McCain is popular among House conservatives, and the idea that they are plotting strategy to win over votes in the House may not sit well with the people whose support they seek.

House Republicans are largely dismissive of advice being handed down from on high, saying they are more interested in hearing what their constituents have to say.

"I pay more attention to what I hear in my district than what I do from various groups," said Rep. Charles Boustany, R-La.