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House Republican leaders on Sunday outlined their caucus game plan for a critical next few months and beyond, suggesting a potential compromise on the sequester before an October deadline and a final vote on immigration reform.

House Majority Leader Eric Cantor suggested that congressional Republicans are open to a compromise to end the deep, undiscerning cuts to the federal budget known as sequester but said the deal would require Democrats agreeing to entitlement cuts.

The Virginia Republican’s statement on “Fox News Sunday” knocks down criticism that his party wanted the cuts and is determined to keep them when Congress returns next month to negotiate a budget deal before the September 30 deadline.

“It’s a default mechanism,” Cantor said about the sequester cuts, which kicked in this spring after Washington failed to agree on a more measured approach. “It’s not the best solution.”

However, Cantor’s apparent signal that Republicans are open to a deal is unlikely to ease fears about a failed compromise and potential Oct. 1 government shutdown, considering President Obama has signaled his unwillingness to further cut entitlements, which include Medicare, Medicaid and Social Security.

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    “We’ve always said the president can join us,” Cantor said. “We shouldn’t be for a government shutdown. We hope we will find common ground.”

    Cantor also defended House Republicans’ efforts last week to pass a series of bills known as “Stop Government Abuse" legislation, instead of focusing on deadlines for the budget and increasing the federal debt limit and presenting counter proposals to Obama’s renewed job creation pitches.

    “First of all, government doesn’t create jobs, the private sector does,” Cantor said.

    However, he argued, the bills are indeed jobs-focused because they are intended to “stop burdening our economy.”

    One of the bills would keep the embattled IRS from being involved in the president’s health care law, which largely takes effect in October.

    Cantor suggested a lack of confidence in the federal government among business leaders and other Americans has led to a slow economic recovery, marked by more new part-time jobs than full-time ones.

    Maryland Democratic Rep. Elijah Cummings last week accused House Republicans of using the series of bills to play “partisan games,” instead of creating jobs before the five-week August recess.

    On the issue of whether the House will have a full vote this fall on immigration reform, as Wisconsin Republican Rep. Paul Ryan recently said, Cantor said only that the chamber will have a vote of on a series of bills “at some point.”

    Ryan, chairman of the House Budget Committee, made clear Sunday that his party wants to get rid of ObamaCare.

    However, using a government shutdown is the wrong tactic because only budgets for government agencies will lose funding, not entitlement programs, which would include ObamaCare, he said.

    “Republicans want to repeal and replace ObamaCare,” Ryan told CBS’ “Face the Nation." "So it's not a matter of whether or not we want to get rid of ObamaCare. We do... It's just not that simple and easy.”

    He said the better strategy is delaying the law, following previous votes to delay parts of it, and that such an effort already has Democratic support.

    “So I think there's going to be a better strategy to actually achieve our goal of ultimately delaying it, ultimately replacing ObamaCare,” Ryan said.

    He also appeared to have reassessed earlier views on the National Security Agency collecting data on Americans’ phone and Internet use as part of it efforts to track terrorists.

    Ryan suggested that after learning more about the programs that Congress should reauthorize but reform them to protect civil liberties.

    He also disagreed with suggestions that Republicans must help pass immigration reform to survive politically.

    “We should approach this issue on what we think is the right thing to do, what's the right policy,” he said. “We don't support the (recently pass) Senate bill. We have been listening to the American people. So what we're going to do is take a step-by-step approach to get immigration right, not a big massive bill but separate bills so people know what's in these bills.”