A Democratic bill to overhaul the nation's welfare system survived its first crucial test yesterday as the House, 213 to 206, approved a resolution sending the bill to the floor, despite Republican charges that the multibillion-dollar measure would be debated under a "gag rule."

Not a single Republican voted in favor of the rule, while 36 Democrats joined the Republicans in voting to kill it. A final vote on the resolution is expected today and Republicans are hoping to team up with conservative Democrats to defeat it.

The bill, which would cost $5.5 billion over five years for welfare program changes and $700 million for food stamp improvements, is designed to move welfare mothers into jobs by requiring the states to set up broad remedial education, job-training and job-search programs for those with children 3 or older.

Rep. Thomas J. Downey (D-N.Y.), the bill's floor manager, rejected GOP arguments that the Democratic measure would not achieve its purpose of getting welfare mothers into jobs.

"We say to the mother, 'We want you to work,' " Downey told the House. "We will train you and educate you but you must participate in the program . . . . We will help you" by providing child-care while in training and then a year of transitional child-care after the mother finds a job and works her way off welfare.

In addition, he said, "our bill seeks to make parents more responsible" by strengthening programs to establish paternity and child-support obligations.

Republicans and some Democrats assailed the measure, claiming it would entail huge costs and discourage work rather than encouraging it because some of the work provisions were ill-designed and because several benefit improvements in the bill would make it more attractive to stay on welfare.

"They call the bill pro-work, yet it has five major disincentives to work," declared Rep. Hank Brown (R-Colo.), adding, "The measure that is before the House is opposed to work."

Rep. Bill Frenzel (R-Minn.) charged, "The costs really begin to increase after five years . . . . If you're looking for a way to wreck the budget," he said, the Democratic bill would do so.

Frenzel said that the Rules Committee resolution governing debate was "another outrageous travesty of the House rules" because it allowed only two floor amendments: a GOP substitute costing $1.1 billion over five years and an amendment to shave $500 million from the Democratic bill over five years. The latter was authorized by Democratic leaders in the hope of holding on to wavering Democratic fiscal conservatives.

Republicans and some Democrats had hoped to defeat the resolution governing debate and open the bill to amendments, including a substitute costing $2.4 billion over five years. But Democrats feared that allowing numerous amendments would chop the bill to pieces.