The $3.4 trillion budget deal reached between House and Senate negotiators faces smooth sailing after leaders of the fiscally conservative Blue Dog Democrats said most of their members would vote for it.

The Blue Dogs failed to get Senate Democratic leaders to commit to bringing up a pay-as-you-go bill — their chief demand — but were appeased by letters from House leaders and President Barack Obama backing PAYGO.

“We have to bring the Senate along kicking and screaming,— said Rep. Allen Boyd (D-Fla.), a Blue Dog leader on budget issues. Senators have a hard time realizing “there’s two sides to a balance sheet.—

Congress doesn’t have the discipline to balance the books on its own, which is why it needs a law enforcing fiscal discipline, as it did in the 1990s, Boyd said.

Nonetheless, he said he was “tickled— by the final blueprint and the support in writing for PAYGO rules from Speaker Nancy Pelosi (D-Calif.), Majority Leader Steny Hoyer (D-Md.) and Obama.

Pelosi and Hoyer committed to not bringing up bills addressing middle-income tax cuts, the estate tax, the alternative minimum tax and Medicare reimbursement rates unless they are fully paid for, they include a provision giving PAYGO the force of law or such a measure has already passed.

The Blue Dogs and House leaders repeatedly caved on PAYGO in 2007 and 2008 under pressure from the Senate on issues like the AMT and an expansion of spending on veterans’ education benefits.

But Boyd said the deal that the Blue Dogs struck this year should have a better chance of sticking now that President George W. Bush is out of office. Now, they have a president who not only supports the policy, but “he put it in writing,— Boyd said.

“The conference report is stronger in every way— than the budget that left the House, Boyd added, noting additional trims to discretionary spending and the long-term deficit.

Rep. Baron Hill (D-Ind.), a Blue Dog co-chairman who introduced PAYGO legislation Tuesday, also predicted most Blue Dogs would back the budget after getting the commitments from Pelosi, Hoyer and Obama.