A new plan unveiled on Inauguration Day by House Republicans would postpone any showdown on a debt limit increase until mid-May, a big change for GOP lawmakers who wanted to use the debt limit as a major battle over budget cuts.

"To ensure the complete and timely payment of the obligations of the United States Government until May 19, 2013," reads the new plan that was rolled out just hours before President Obama spoke to hundreds of thousands at his Inauguration.

It was a big change for GOP leaders in the House, who had been making waves in recent weeks about another big time clash with the White House and Democrats over the debt ceiling.

Whether it floats with the Republican rank and file - we will see over the next two days.

As for the President, he made no direct reference to the debt limit in his Inaugural Address; White House officials have made clear in recent days that they will not negotiate with Republicans in any way on a debt limit agreement.

"There was only a quick mention of our deficits," groused Rep. James Lankford (R-OK).

Even with that, Republicans don't seem united over how best to push the President on the issue of debt and deficits when it comes to the debt limit.

We should hear more about the issue of the debt limit and the budget on Tuesday, as House Republican leaders will have their first news conference since late in December, when both parties were locked in their titanic struggle over the fiscal cliff.

Also included in this debt limit plan is another issue, the "No Budget, No Pay" initiative that says if lawmakers can't get the budget done on time, then they won't get paid.

This bill has a bit different solution than what has been previously offered by lawmakers in both parties, as it would withhold the pay of members, since there were Constitutional issues about whether the Congress could legally block lawmaker salaries.

In this instance, lawmakers would not be paid if the House and Senate had not approved the non-binding "budget resolution" by April 15, but not the actual measures - the appropriation bills - that actually do the spending on the federal government.

The "budget resolution" is what Democrats have not acted on since 2009, when they used it to help pave the way for the Obama health reform law.

Even though that resolution was not approved, the House and Senate still managed to pass various spending bills, though never on time and often in a messy year-end jumble where a bunch of budget bills are jammed into one measure.

So, while the Senate has not approved the "budget resolution" in four years, it's not really 100% true to say the Senate hasn't worked on the budget, because either through stop-gap budgets or omnibus budget bills, federal spending has been okayed by lawmakers in both the House and Senate.

The last time the Congress approved the budget bills on time (by October 1) was 1994, while a finalized budget resolution gets done by the April 15 deadline about one out of every six years.

Not exactly a great budget record from either party, to say the least.