Updated

House Speaker Nancy Pelosi said Saturday that she will not cut a deal with a group of anti-abortion Democrats to include tighter restrictions on abortion funding in the final health care bill, suggesting that she believes she has enough votes to pass the legislation without them.

Pelosi told Fox News that there will be no vote on a separate bill adding abortion restrictions as proposed by Rep. Bart Stupak, D-Mich. to the final legislation.

Earlier Saturday, members of the House Rules Committee, which began deliberations that will set the terms for Sunday's expected vote in the full House, told Fox News that no changes would be made to the abortion funding restrictions contained in the Senate version of the bill.

Stupak, who has led the charge to include in the final bill tougher anti-abortion language passed last November by the House, postponed a Saturday morning news conference in which he was expected to announce a deal with Pelosi.

Stupak's office told Fox News that the news conference was postponed due to "scheduling issues," not because there was a breakdown in abortion talks.

A spokeswoman for Stupak added, "discussions are continuing."

Party leaders are considering winning crucial support from abortion foes with an executive order by President Obama.

The order -- which does not require congressional approval -- would be aimed at reflecting long-standing law barring federal aid for abortions except for cases of rape or incest or when the mother's life is threatened.

Democratic Reps. Henry Waxman of California and James Oberstar of Minnesota both said an executive order was under discussion by party leaders.

It was unclear whether the strategy would win support from Stupak.

On Friday, Stupak  -- with eight Democrats and one Republican as co-sponsors -- introduced a resolution that would insert his abortion restrictions as a "correction" to the underlying bill. That would have added new complications to the already complex strategy Democrats are pursuing to pass the bill, requiring additional floor votes on a highly charged issue.

Stupak and his backer were hoping they had enough leverage to force the leadership to yield to their demand.

But Waxman said Saturday that "the likely outcome" is that Pelosi will move ahead without the votes of the anti-abortion group.

Waxman is chairman of the House Energy and Commerce Committee and he helped write the 10-year, $940 billion bill.

The current legislation would allow private insurance plans operating in a new insurance marketplace to cover abortions, provided they do not use taxpayer funds.

What makes that tricky is that many of the plans' customers would be receiving federal subsidies to help pay their premiums. So the legislation requires plans offering abortion coverage to collect a separate premium from their policyholders. Those separate checks would have to be kept in a different account from money for other health care services.

Federal law since the 1970s has forbidden the use of taxpayer funds to cover abortions except in cases of rape, incest or to save the life of the mother. But many private insurance plans cover abortion as a legal medical procedure. How to deal with the divisive issue in health care overhaul was a source of controversy from the beginning.

Fox News' John Brandt and The Associated Press contributed to this report.