The president urged the state executives particularly the Republicans to lobby members of Congress to avoid the sequestration with a new deal to help reduce the national debt of more than $16 trillion.
Not all Republicans were convinced, saying Obama could offset the $85 billion in cuts by cutting less than 3 percent of the federal budget. Louisiana Gov. Bobby Jindal, a potential 2016 Republican presidential candidate, said it's time for Obama to "stop scaring people" and instead "show leadership."
Obama wants a debt reduction deal that includes both budget cuts and higher taxes on the wealthy, in the form or closing loopholes and deductions.
Republicans oppose any tax increase, saying Obama got higher tax rates on the wealthy as part of last month's "fiscal cliff" deal a view shared by some of the GOP governors who met with the president at the White House.
Republicans such as Jindal and Wisconsin Gov. Scott Walker said tax hikes could slow the economy just as much as some arbitrary tax cuts. They pointed out that the fiscal agreement ended a 2 percentage point cut in the payroll tax, increasing that levy for wage-earning Americans.
"This administration has an insatiable appetite for new revenues," Jindal said.
Vice President Biden also addressed the National Governors Association's gathering, appealing to what he described as their bipartisan spirit and willingness to get things done. Biden, a senator for 36 years before becoming vice president, attributed the latest budget standoff in Washington to an "intense partisanship, that the likes of which, in my career, I've only seen the last couple of years."
Obama's remarks to the governors were part of an ongoing effort to warn Congress about the impact of the sequestration briefings.
At a White House news briefing, Homeland Security Secretary Janet Napolitano said budget cuts would weaken border security, slow responses to emergencies, delay container inspections at ports, and lengthen lines at airport security screenings and customs checks.
"The lines over the next few weeks are going to start to lengthen," Napolitano said.
Beyond the sequester, Obama told the governors he wants to be their "partner" on two major legislative items, infrastructure and education.
Repairing and expanding the nation's system of roads, bridges, tunnels, railways and airports should be a bipartisan endeavor, Obama said.
As for education, Obama said he wants states to help him achieve his goal of preschool for all of America's children.