Correction: An earlier version of this story misidentified the committee on which Sen. Orrin Hatch (R-Utah) is ranking Republican. It is the Finance Committee. The story has been corrected.

Politicians in both parties have repeatedly called for a simpler tax code with fewer of the loopholes, credits and deductions that make tax filing a nightmare and deprive the government of billions in revenue.

But when the Senate votes Thursday on a portion of the president’s job bill — one with broad bipartisan support — a key element of the measure will be a brand-new tax credit: for businesses that hire unemployed veterans.

Tax experts say the hiring credit is a particularly stark example of how irresistible the tax code has become for politicians seeking to advance popular policy goals. And, they say, it shows how difficult it would be to weed out popular credits and deductions.

“It’s ironic, and it’s incongruous,” Steve Bell, senior director of the economic policy project of the Bipartisan Policy Center, said of consideration of a new tax credit while tax reform gains steam.

“Tax entitlement reform will be tougher than direct spending entitlement reform,” he added. “Because they all got in there for a reason . . . They got in there because big groups of people benefit from them.”

The most expensive tax breaks inserted into the code by lawmakers don’t benefit popular targets like gas companies or corporate jet owners, but instead assist middle-class families. Those breaks include the deduction for mortgage interest that helps homeowners and an exemption on taxation of health-insurance premiums paid by employers for their workers.

The beneficiaries of the latest tax credit would be unemployed military veterans, a group widely considered deserving.

Unemployment among veterans who left active duty in 2009 or later has risen in recent months and stands at 12.1 percent — more than 3 percentage points above the jobless rate for civilians.

Thursday's vote will come on the eve of Veterans Day, and if the House approves the credit as well, it will probably prove almost politically impossible to eliminate.

The credits are part of a broader veterans package that also includes new money for training programs to help service members transition to the civilian workforce and to help retrain older unemployed veterans.

Businesses would receive a tax credit of as much as $9,000 if they hired a disabled veteran who had been out of work for more than six months. They could get a $5,600 credit for hiring any veteran unemployed for at least six months and $2,400 for hiring a veteran out of work for at least a month.

The estimated cost of the package, to be offered as an amendment to another measure Thursday, is $200 million. It would be paid for by delaying a planned reduction in fees on home loans guaranteed by the Department of Veterans Affairs, and by other fees.

“Veterans can read this as the country still having their backs,” said Tom Tarantino, a senior legislative associate for the Iraq and Afghanistan Veterans of America.

The tax credits were included in President Obama’s $447 billion American Jobs Act, blocked by the Senate last month.

“Our veterans did their jobs. It’s time for Congress to do theirs,” Obama said Monday, urging approval of the tax credits.

Republicans, too, have embraced the hiring tax credit and called on Democrats to stick to similar job-creation ideas that could achieve bipartisan backing, instead of continuing to push pieces of Obama’s jobs plan that the GOP opposes.

“What this credit suggests is that Congress remains addicted to delivering private-market intervention through the tax code at the same time as it tells us it’s going to get clean and sober,” said Edward D. Kleinbard, who was chief of staff for the Joint Committee on Taxation and now teaches at the University of Southern California’s Gould School of Law.

But senators who have supported reform said they could not turn their backs on needy people while the debate over how to fix the tax system drags on.

“People do want to help the veterans as much as we possibly can,” said Sen. Orrin G. Hatch (R-Utah), the ranking Republican on the Senate’s Finance Committee. Hatch said that the tax system must be broadly reformed and that credits shouldn’t be avoided on a “a scattered basis.”