AUSTIN, Texas—Gov. Rick Perry was expected to begin weighing a Republican presidential bid this week but instead found himself enmeshed again in the battle over the state budget.

A filibuster by Senate Democrats before the end of the 2011 legislative session on Monday derailed a $15 billion, two-year cut in state spending backed by the governor and forced him to call a special session that started Tuesday.

As for his possible presidential ambitions, which he had floated Friday, Mr. Perry told reporters Tuesday afternoon, "Talk to me after the session is over with."

Smooth passage of the budget, which had been hailed by conservatives as containing the first overall spending cuts in half a century, would have been an extra presidential selling point for Mr. Perry, adding "fiscal conservative" to his tea-party bona fides as an advocate for states' rights. But Democrats had balked at a $4 billion cut in aid to local school districts, and predicted on Monday that voters would eventually be angered by the size of the cuts, which would top 3% next year and almost 6% the following year.

Republicans, who have a large majority in the legislature and plan to use special-session rules to bar any filibuster, are likely to approve the cuts—and move on to other agenda items.