The House Ways and Means Committee is scheduled to meet Thursday to begin drafting a tax bill, and members said their task will be made easier by the lower increases required under budget legislation that President Reagan now says he will sign.

Committee members said they are optimistic they can draft a bill to collect $12 billion in new taxes in 1988, as required by the deficit-reduction measure passed last week.

The previous budget outline, abandoned over the summer, had called for $19.3 billion in higher taxes, a figure that even Chairman Dan Rostenkowski (D-Ill.) said was nearly impossible. Even raising $12 billion will take concerted effort and some temporary setbacks, legislators said.

The lower revenue target -- some disagreement remains over the precise amount that must be raised -- puts this year's tax bill in the same magnitude as the 1982 and 1984 laws, which closed some business loopholes but had little impact on average taxpayers. Tax writers said the smaller goal means they may be able to craft a "cats-and-dogs" bill that does not significantly raise such visible levies as excise taxes on alcoholic beverages or gasoline.

"This is a case where less is beautiful, as Jerry Brown used to say," said Rep. Willis D. Gradison (R-Ohio). Like some other Ways and Means Republicans, Gradison said he is willing to consider supporting a tax bill of this size, although his decision will depend on what it includes. Nearly all House Republicans had vowed to oppose tax increases in the $19 billion range, but some may support a smaller tax increase, especially if the alternative is the automatic spending cuts mandated by the budget legislation.

Rostenkowski does not plan to propose his own tax plan, but wants one to evolve through the committee's deliberations, scheduled to last about two weeks. The idea, aides said, is to eliminate the least popular proposals and then approve what remains.

Some of the elements likely to turn up in a House tax bill are well-known. Rostenkowski said he wants to start with the revenue-raising measures proposed in Reagan's budget, such as extending the payroll tax for Medicare to state and local employes and requiring employers to pay Social Security taxes on the money their service workers receive as tips.

Other tax increases almost certain to be seriously considered include closing a loophole related to estate taxes and extending the 3 percent federal telephone tax, which is scheduled to expire at the end of this year. Those items and the Reagan proposals, plus a few other small increases, would collect roughly $6 billion next year.

Coming up with the next $6 billion will be more difficult. There is no shortage of choices: The committee has before it a 291-page list of options ranging from higher tax rates on upper-income taxpayers to cutbacks in partnership tax shelters. But many either are politically difficult or would bring in very little revenue.

"I think it is going to be very painful," said Rep. Barbara B. Kennelly (D-Conn.). "There will be a few days when we hit a brick wall."