House Republicans want to spend this short congressional week hammering President Barack Obama and Senate Democrats over the budget, hoping to ride the momentum of their “no budget, no pay” ploy.

The House will take up a measure that would force the president to identify the date his budget would balance when he submits the spending blueprint to Congress later this year. If it does not do so, he would have to submit a new budget that does.

The idea came out of the office of Majority Leader Eric Cantor, R-Va., according to GOP leadership sources, though it is sponsored by Budget Vice Chairman Tom Price of Georgia.

By law, the president must submit his budget by Monday, but acting Office of Management and Budget Director Jeff Zients sent a letter to Budget Chairman Paul D. Ryan, R-Wis., last month informing him that the budget will be delayed because of late passage of a fiscal-cliff deal. Republicans are eager to hammer Obama on that point.

Obama met the deadline only once in his first term, and Cantor said in a statement that the latest tardy budget is “another signal he is not serious about solving our nation’s spending problem.”

Cantor continued: “That is unacceptable. Even the budget he eventually submitted last year never achieved balance.”

The House approved a bill last month mandating that if either chamber does not pass a budget by a certain date, members of that chamber would have their pay withheld.

Getting the Senate to agree to that measure was a start, Speaker John A. Boehner of Ohio said in a Feb. 1 statement.

“With this measure, we are giving the president a chance to kick his habit of submitting budgets that spend, tax, and borrow too much,” the speaker said. “Given that the president’s budget will be late, it may as well be right.”

A spokesman for the president did not return a request for comment. Senate Democrats, meanwhile, are unlikely to take up the Price bill.

For their part, House Democrats do not seem to be taking the measure very seriously.

“This is just another gotcha gimmick,” Rules ranking member Louise M. Slaughter, D-N.Y., said in a statement. “Last week they tried to blame the Senate; this week, it’s all the President’s fault. We need to put an end to the blame-shifting and legislative gimmicks if we want to put our fiscal house in order and put people back to work.”

Still, the fact that House Republicans are pushing the bill, especially in the face of much graver issues in the same vein that must be dealt with in the next few months, signals that the GOP believes it is in its best interest to strike first on budget battles.

The No Budget, No Pay Act has already set the tone for the budget debate moving forward, forcing Senate Democratic leaders to go along. The Senate passed the bill Jan. 31.

“No budget, no pay was such a huge victory for us,” one GOP aide said. “We’re going to continue to go on the offense.”

The fact that Price is the lead sponsor is also notable, considering the recent, bruising race for the GOP conference chairmanship, which he lost to leadership favorite Cathy McMorris Rodgers of Washington.

It signals that the Georgia Republican’s role in messaging, which had been substantial, might not diminish after all.

And the bill, even if it does not pass the Senate, could be a notch in his belt should he decide to run to succeed Sen. Saxby Chambliss, R-Ga., who announced recently that he will retire at the end of his term.

“No one ever thought Mr. Price was anything other than a valuable member of the conference,” a GOP leadership aide said. “We’ve always worked with him. He’s been in a lot of meetings with leadership.”

On Monday, the House Rules Committee will vote on Price’s measure, and it will be on the floor Wednesday, according to Cantor’s office.

The Wednesday vote will be the last of the week, as the House breaks for the Democratic retreat in Leesburg, Va., and a conservative retreat hosted by The Heritage Foundation in Baltimore.