But he praised Mr. Camp for “coming forward with a piece of legislation.”

Mr. Camp said nonpartisan economists at the congressional Joint Committee on Taxation had estimated that streamlining the tax code would increase the size of the economy by $3.4 trillion over the next decade. “This will lead to nearly two million new jobs — and producing up to $700 billion in additional federal revenues,” he wrote in an op-ed article published online Tuesday night by The Wall Street Journal.

Image Dave Camp of Michigan wants to simplify the tax code. Credit... Chip Somodevilla/Getty Images

He went on to predict that families at the median income level — $51,000 for a family of four — would “have on average an extra $1,300 in their pocket at the end of the year.”

Mr. Camp is also set on Wednesday to shepherd a bill through the House that would stop new Internal Revenue Service regulations of political “social welfare” groups. That underscores a quandary facing House Republican leaders as they head into the midterm elections: Should they limit their agenda to political bills tailored to aid Republican campaigns like the I.R.S. bill, or should they take big risks on ambitious policy proposals, like simplifying the tax code?

Intraparty controversies were precisely what Speaker John A. Boehner of Ohio had hoped to avoid this year when he shelved a broad immigration push, then whisked through an increase in the debt ceiling, relying almost entirely on Democratic votes.

Even those who believe that Mr. Camp’s proposal has little chance this year say that his so-called discussion draft will serve as a test of support among fellow Republicans who favor tax changes in theory but often balk at the trade-offs required. Those Republicans are especially hesitant to act on a bill that is unlikely to make it through the Senate, which is controlled by Democrats. If Mr. Camp’s plan fails to attract a Republican majority, it is coming early enough in the year that it is unlikely to have lasting ramifications in the midterm elections.

House leadership aides told Mr. Camp in November that he needed to find a Democratic partner other than Senator Max Baucus of Montana, the chairman of the Senate Finance Committee at the time, who had been working with Mr. Camp on a tax code overhaul. But Mr. Camp failed to do so — and now Mr. Baucus is ambassador to China. Senator Ron Wyden, Democrat of Oregon, now leads the Finance Committee.

Democrats are expressing their frustration with how the tax plan is being rolled out. Democratic aides say that unlike their Republican colleagues on the Ways and Means Committee, Democrats have not been briefed on any of the plan’s details, and they did not receive a letter that went out to all the Republican members last week alerting them of the draft legislation to be released on Wednesday.