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State of the Union addresses are usually packed with promises and lofty goals. But President Obama's pledge Tuesday night to push a raft of spending proposals without adding "a single dime" to the deficit appeared to make little sense to Republicans.

"Under President Obama, the national debt has increased by 58.6 trillion dimes," a video swiftly released by the Republican National Committee reminded viewers.

The video showed clip after clip of Obama vowing in past addresses that his proposals would be paid for. The State of the Union address was the latest installment.

Obama said Tuesday his proposals to fuel economic growth are "fully paid for" and added: "Nothing I'm proposing tonight should increase our deficit by a single dime."

Ultimately, it's difficult to pin down whether any particular spending program is paid for. One proposal may be offset with cuts or tax increases elsewhere in the budget. But then other programs in turn do not get paid for, helping result in $1 trillion-plus deficits over the last four years.

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Obama did not get into many specifics Tuesday night on how his ideas -- should the Republican-controlled House even bring them to a vote -- would be offset, other than by calls to close tax loopholes and, in at least one case, attract some private capital.

That program was called the "Partnership to Rebuild America," which Obama said would attract private dollars to upgrade ports and modernize pipelines and schools. He also, though, proposed a "fix-it-first" program to put Americans to work on "urgent repairs" like structurally deficient bridges across the country. And he reiterated support for the previously proposed American Jobs Act, which included $50 billion in infrastructure spending. Both those would use taxpayer dollars.

To Republicans, infrastructure spending is code for more stimulus, which is precisely what House Speaker John Boehner labeled it in a statement Tuesday night. Sen. Marco Rubio, R-Fla., who delivered the GOP response, said Obama's solution "to virtually every problem we face is for Washington to tax more, borrow more and spend more."

Obama's proposals went beyond roads and bridges to include the creation of "manufacturing hubs" across America.

He called for more "investments" in science and technology, as well as legislation to address climate change and policies to generate more clean energy. In the past, the latter has translated to subsidies for alternative energy companies.

And the president called for legislation to give homeowners a chance to refinance their mortgages and announced a policy to "reward schools that develop new partnerships with colleges and employers."

The bulk of these proposals would cost money, though how much is unclear, as is how they would be offset. The president also called for an increase in the federal minimum wage from $7.25 to $9 an hour, and tying increasing to rises in the cost of living. Obama and others pitch this as a way to help millions of families and lift many out of poverty. But some business groups and Republicans say this, too, comes at a cost -- and has the potential to backfire by resulting in job loss.

The Employment Policies Institute claimed the move would hurt the economy, pointing to one study that found an earlier federal increase proposal could cost at least 467,000 jobs.

Obama in his speech, though, defended and promoted these "investments" and, while stressing the need to rein in the budget, said austerity in itself cannot be Washington's goal.

"Most of us agree that a plan to reduce the deficit must be part of our agenda. But let's be clear: deficit reduction alone is not an economic plan," Obama said.

Regardless of whether Obama's proposals add to the deficit, he is sure to face a mixed reception in putting the emphasis on new government programs when many -- particularly House Republicans -- are more interested in paring back the spending out of Washington. Some argue this could even help the economy by sending a signal that the federal government is at last tackling the budget deficit.

Obama acknowledged Tuesday that the "biggest driver" of long-term debt is the rising cost of health care. He said America "must embrace the need for modest reforms" but "we can't ask senior citizens and working families to shoulder the entire burden of deficit reduction while asking nothing more from the wealthiest and the most powerful."

He called for a "balanced approached" to closing the deficit that includes cuts and tax increases, though Republicans say the debate over tax hikes is over.

He said he would back some Medicare reforms that reduce subsidies to prescription drug companies and "ask more from the wealthiest seniors."

The president, while spending the bulk of his address on economic and budget issues, was perhaps most impassioned when talking about gun legislation. With many victims of gun violence and their families in the audience Tuesday night, Obama claimed broad support for strengthened background checks and said a range of measures -- like an assault-weapons ban and a ban on high-capacity magazines -- should get a vote in Congress.

"Gabby Giffords deserves a vote. The families of Newtown deserve a vote. The families of Aurora deserve a vote," Obama said.

The president also vowed to sign immigration legislation that achieves certain goals -- like a "responsible pathway to earned citizenship." The immigration legislation may be easier to achieve than any comprehensive gun regulation package, as lawmakers on both sides of the aisle are already working on the framework for an immigration bill.

On foreign policy, the president declared Tuesday that he would withdraw 34,000 troops from Afghanistan over the next year, which represents about half the force in the country now.

The president spoke Tuesday as the economy showed mixed signs of recovery. While hiring has picked up since the sluggish 2009-2010 period, the unemployment rate ticked up again last month. While the stock market appears to be steadily improving, economic growth remains tepid -- the Commerce Department estimates the economy actually shrank by .1 percent at the end of 2012.

But Obama and the rest of Washington are facing a balancing act, with another looming deadline demanding that Washington take serious steps to address the federal deficit.

Automatic spending cuts are poised to hit March 1 unless a deal is reached to replace them. Some Republicans are talking about letting the cuts simply take effect, though the Pentagon will bear the brunt of the hit. Other Republicans want to replace the scheduled cuts with a separate package of cuts.

Obama, to the chagrin of Republicans, wants to include tax increases in any package. He has also urged Congress to draft a short-term bill if no deal can be reached by March 1. Republican leaders have largely bristled at this demand.