WASHINGTON — House Republican leaders appeared ready to buck their Tea Party flank on Wednesday as they closed in on a spending deal to avert a government shutdown and prepared to call a vote next week.

If the plan by Speaker John A. Boehner and his leadership team prevails, it will be a significant victory for Republicans eager to avoid the kind of bitter and politically harmful fight that led to a 16-day shutdown last year.

But many conservative Republicans were venting their frustrations in private meetings and news conferences at the Capitol as they called on their colleagues not to ignore the anger from their base over President Obama’s decision to defer deportations for millions of illegal immigrants.

It is a fight Mr. Boehner is willing to have.

He and his allies believe they will find themselves in the uncomfortable position of having to rely on Democrats to pass the spending bill through the House because of the number of Republicans who will vote against it. But the trade-off is one the speaker can accept: He may draw the ire of conservatives and Tea Party groups, but he will demonstrate to voters that Republicans can be pragmatic and not beholden to their most far-right elements.