House Republicans do not have enough support to pass their debt-ceiling increase plan on their own, a top conservative said Tuesday as his party’s leaders tried to cobble together a coalition of Republicans and Democrats to put the bill over the top.

“There are not 218 Republicans in support of this plan,” Rep. Jim Jordan, an Ohio Republican who heads the powerful conservative caucus in the House, told reporters Tuesday morning.

If Mr. Jordan is right, that would mean Speaker John A. Boehner would have to rely on Democrats to pass the $1.2 trillion spending cuts plan — support Democrats’ top vote-counter said he’ll be hard-pressed to gain. Minority Whip Steny H. Hoyer said “very few” Democrats will vote for the Boehner plan, though he acknowledged there could be some.

A vote in the House is expected Wednesday, and Republican leaders are trying to round up enough support to pass their version. They hope that if it can pass the House, that will pressure Senate Democrats to drop their alternative and accept the GOP’s plan.

Mr. Boehner’s bill would reduce future discretionary spending by $1.2 trillion, grant an immediate debt increase of $1 trillion, and set up a committee to work on trillions of dollars in future deficit reduction either through more spending cuts or tax increases, which would then earn another future debt increase. It would also require both the House and Senate to hold votes on a balanced budget amendment to the Constitution.

But conservative Republicans in the House, many allied to the tea party movement, said they don’t just want votes on the amendment, they want an assurance it will be sent to the states. Mr. Jordan and other conservatives said they would prefer the Senate vote on the debt increase the House passed last week, that includes deeper spending cuts and requires both chambers approve a balanced budget amendment and submit it to states for ratification before any debt increase happens.

Both the Heritage Foundation and Club for Growth, two key conservative activist groups, are also urging a “No” vote and said it will be one of the key votes they use in their annual lawmaker scorecards.

Mr. Boehner said Tuesday that his plan is the only option that can bridge party differences and win enough support to pass Congress.

“We have a bill that is a reasonable approach negotiated with the Senate leadership that really is commonsense,” Mr. Boehner said. “There’s more cuts in spending than you have an increase in the debt limit. It has real caps and a real process for cutting spending before the end of this year. And it provides for — I think — the best effort to get a balanced budget amendment enacted into the Constitution.”

On Monday President Obama called for voters to call Congress and demand a compromise bill, and on Tuesday offices said they have been inundated.

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