Former President Barack Obama's $400,000 speaking fee has prompted another attempt to strip his pension, says House Oversight Chairman Jason Chaffetz.

Chaffetz, R-Utah, along with Sen. Joni Ernst, R-Iowa, say they will reintroduce the Presidential Allowance Modernization Act this month, according to a USA Today report on Wednesday. The legislation, which was vetoed by Obama in July of last year, would cut allowances of the ex-presidents.

At the time of the veto, Obama argued that such a bill would impose financial burdens on former executive branch employees.

"It would impose onerous and unreasonable burdens on the offices of former presidents, including by requiring the General Services Administration to immediately terminate salaries and benefits of office employees and to remove furnishings and equipment from offices," Obama wrote in his veto message.

He added that he would be open to reconsidering a revamped version of the bill if it addressed his concerns.

Congress never attempted to override the veto.

The original bill allowed a former president a lifetime annual annuity of $200,000, along with an additional annual monetary allowance of $200,000, "each adjusted annually for cost-of-living increases as provided by the Social Security Act."

However, the amount of allowance would be reduced if a former president's adjusted gross income in a taxable year exceeds $400,000.

Obama has come under heavy criticism, even from fellow Democrats, lately for his reported $400,000 speaking fees, equal to the salary a president makes per year.

Chaffetz, in tweeting out the USA Today report, with the headline, "Obama's $400,000 speech could prompt Congress to go after his pension," added his own message: "Yes, it will."

The top Democrat on the oversight panel, Rep. Elijah Cummings, D-Md., was a co-sponsor of the original bill. A spokesperson from his office said the congressman would be open to backing another push.

"Cummings definitely supports the concept, and if we can work out the technical issues with the bill that arose late in the last Congress, we expect he would strongly support it again," spokeswoman Jennifer Hoffman Werner told USA Today.