Congressional Republicans are protesting a recent ultimatum by President Obama to veto the introduction of any new annual spending bills that use the GOP's budget proposals unless a broader budget agreement can be reached.

While acknowledging the prospect of agreement between the Republican-controlled House and Democratic majority in the Senate is "a daunting challenge," in a letter to the president Thursday House Speaker John Boehner accused him of threatening a government shutdown with the position, asking to keep the two issues separate so as not to jeopardize party negotiations over a budget deal.

"At a time when such delicate discussions are underway, the introduction by your administration of such an explosive new dynamic [...] needlessly injects a new element of uncertainty into our economy and further jeopardizes hopes for a bipartisan agreement," it reads.

The speaker also claimed the president's stance contradicted statements he made at a March press conference when he said "there's no reason why we should have another crisis by shutting the government down in addition to these arbitrary spending cuts," referring to the across-the-board package of budget reductions known as the sequester.

Related: Sequestration Here to Stay, or On It's Way Out?

In a statement on Monday the White House announced in broad terms that the president's advisers would "recommend" a veto of any spending bill that used Republican budget proposals as a framework, referring to two bills that passed the House later in the week. One funded the Department of Homeland Security while the other provided funding for the Department of Veterans Affairs and military construction projects.

Although both bills made use of Republican budget proposals to keep the sequester in place, the latter legislation passed with an overwhelming and veto-proof majority of 421-4, which includes the vast bulk of Democrats in the House of Representatives.

Meanwhile an Obama spokesperson says the presidential veto threat shouldn't be translated into one of government shutdown, but rather used to frame their position that the GOP's cuts would harm needed domestic programs.

"The administration made one thing very clear this week: we simply won't sign into law the Republican budget, which would drastically slash the investments the middle class, seniors and our economic growth depend on," writes Amy Brundange. "The president's policies, including signing into law over $2.5 trillion of deficit reduction, have contributed to the most rapid decline in the deficit since World War II."

Related: Sequester Seems to Have Emboldened, Not Hurt, Some Republicans

The Republican budget, written by House Budget Committee chairman Rep. Paul Ryan, calls for continuing the current federal spending levels set by sequestration while shifting about $30 billion to the Defense Department from non-military programs.

Should a budget negotiation stall it does not necessarily mean a shutdown is imminent. Congress would likely pass what is called a continuing resolution, temporary measures designed to fund the government for a limited time. The practice has become commonplace in recent politics. Last month the Senate passed such a stopgap to fund the government until fall.