Over three decades, Sen. Orrin Hatch has labored unsuccessfully for a Balanced Budget Amendment. The Senate last passed such a measure in 1982, only to be disappointed by a Democrat-controlled House. The tease hit its apex in 1997, when the Utahn cobbled together 66 votes — one aye short of the constitutional requirement. “Like Charlie Brown with the football, we kept trying,” he laments in his memoir.

With fiscal hawks roosting in both chambers, Hatch, the ranking Republican on the Senate Finance Committee, is itching for another round. This week, along with Sen. John Cornyn (R., Texas), he will unveil a revamped proposal. The pair’s amendment will mandate the federal budget not to exceed total revenues, cap federal spending at 20 percent of gross domestic product, and require a two-thirds vote (in both the House and the Senate) for net tax increases. The legislation will also require the president to submit a balanced budget to Congress each fiscal year.

As the federal government nears its $14.3 trillion debt ceiling, a “great constitutional debate,” Hatch declares, is necessary. “Let’s put the screws on the big spenders,” he says. “We are facing a fiscal crisis and excuses are unacceptable.”

Cornyn agrees. “We don’t have to extend the debt ceiling for a year; we could do it for a month,” he says. “The question is, what price is the Democratic leadership in that Senate willing to pay in order to get a longer extension of the debt ceiling? Personally, I think that a vote on a balanced-budget amendment is one of the prices we should exact for a vote on the debt ceiling.”

Pressuring President Obama to move beyond scrambled talking points, especially in his post–State of the Union glow, is instrumental. “We have witnessed a colossal spending binge out of this White House,” Hatch sighs. “They have put forward budgets that double the deficit in five years and triple it in ten.” With Gene Sperling, Obama’s top economic adviser, having worked with congressional Republicans on a balanced-budget compromise during the Clinton years, there may be an opportunity for more than crosstalk.

“When we had these grand budget compromises in the 1980s and 1990s, spending was reduced, taxes were raised, and the crisis was stalled, but only for a short period of time,” Hatch observes. “Over time, the tax increases remained, but the spending began to increase almost as soon as the deals were finished.” A constitutional amendment, he argues, is the medicine for this Beltway ailment.

Cornyn says the tax deal Senate Republicans made during the lame-duck session enables them to frame their case around spending. “Usually, when we talk about balancing the budget, there is a fight between people who think we need to raise taxes and people who think we need to cut spending,” he says. “Having resolved the tax issue for two years, we can now focus on spending, which has always been the primary culprit.”

In the GOP cloakroom, the Hatch-Cornyn initiative is gaining steam. Twenty senators, including veteran John McCain of Arizona and freshman Roy Blunt of Missouri, have signed on. So have Americans for Tax Reform and the American Conservative Union, two influential outside groups. “I think this has a good chance of passing,” Cornyn says.

Hatch and Cornyn, however, are not the only Senate Republicans who will propose a balanced-budget amendment this month. Rand Paul, a Kentucky freshman and founder of the Tea Party Caucus, is readying his own package, which will couple $500 billion in federal budget cuts with a balanced-budget amendment.