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The other two remained without an expiration date. In the 1980s, a Texas college student, Gregory Watson, began to rally support to get enough states to ratify the pay-raise amendment. In 1992, Michigan put it over the three-fourths threshold.

Mr. Watson told The Washington Times that he thinks the Republican proposal is constitutional.

“Nowhere in such a proposal do I see any violation of the terms and provisions of the 27th Amendment,” Mr. Watson said in an email. “Such a proposal does not ‘vary’ the dollar amount of compensation to members of Congress, the proposal merely delays the disbursement of that dollar amount.”

The budget is always a major fight in each chamber. It forces the majority party to take a series of tough votes that are always used against lawmakers in elections.

House Republicans passed a budget in each of the past two years, but Senate Democrats haven’t written one since 2009 as Majority Leader Harry Reid tried to shield his members from those tough votes.

That has become a major annoyance to the GOP, and after the tax-hike bill to which Republicans agreed earlier this year, they said they are intent on making Senate Democrats take difficult votes.

“The last time they passed a budget, the iPad hadn’t been introduced,” said Rep. Kevin McCarthy, California Republican and the majority whip.

Mr. Reid, asked about the Republican debt and pay bill, ignored the budget provisions and focused instead on the short-term debt extension.

“I’m very glad that they’re going to send us a clean debt-ceiling bill. The other stuff on it, we’ll approach that when we need to,” he said.

The White House took the same approach, releasing a policy statement generally backing the debt-limit extension, but remained silent on the budget portions.

In 2011, a fight over the debt ceiling nearly ended in a partial government shutdown, and was averted by a last-minute deal that granted Mr. Obama a huge debt hike, but also set in motion the automatic spending cuts, or “sequesters,” that still haunt Congress.

Republicans framed this debt extension as a chance to get some breathing space and take another crack at spending and tax reforms. They said it is the first step in a push to balance the budget within 10 years.

But some conservatives said they won’t be able to vote for it, arguing against any debt increase — even coupled with the budget and pay provisions.

And it marks a retreat from Mr. Boehner’s stance that every debt increase be accompanied by a dollar-for-dollar match in spending cuts.

“I’m glad the debt ceiling is not an issue that we need to address now,” Mr. Reid said. “The debt ceiling is not going to kick in for a while. We have many months of work through this.”